Then the normal movement stops. We enter a zone of emptiness and immobility. The few cars on the road all stop. We wait at endless red lights for no traffic to pass. The driver, an elderly Korean who many years ago followed his sons out when they came to study at the University of Canterbury's engineering faculty, and who now belongs to the highly visible Korean community in this variously peopled small city, looks unsurprised.

Something else happens. As we move ever more slowly from green periphery to business centre, the landscape opens out. Behind high cyclone wire fences, all you see is rubble-strewn open space. There are a few medium-high office blocks standing arbitrarily in this empty flatness and, like the teeth in a centenarian's mouth, they mainly emphasise what's missing.

We pull up in what is nominally Cathedral Square, the city's geographical and historical centre. On its short run, the taxi has racked up an astronomical fare. My hotel is a neat and anonymous pale block, recent, undamaged and evidently well built. We're in the middle of nowhere.

I chose this place because it stands on the patch of ground once occupied by Warners Hotel, where I stayed at the age of 12 on my only previous visit to the city. Warners was a grand 19th-century establishment. We ate roast beef and my father drank whisky and I sat by a log fire reading the more macabre stories of Robert Louis Stevenson. A few years later the Beatles stayed there, too.

Warners stood almost directly opposite ChristChurch Cathedral, a mock-Gothic building in blue stone, massive but not enormous, the material and spiritual epicentre of this mock-English colonial city that was founded here in 1850. Warners and the cathedral were what Christchurch was about. A wing of Warners lasted until the earthquake three years ago, adjoining today's Novotel as its heritage extension. Then it became rubble, and was cleared away for yet more of the car parks and linked pedestrian areas that surround my hotel and a few other surviving buildings.

Flatness is everywhere. The cathedral is still there, behind a safety fence. The great steeple is down and one end has collapsed and it looks like a dead blue whale disintegrating on a beach. You can see why the Church of England and its bishop Victoria Matthews want it quietly gone. It reeks of death and the past. They are opposed by die-hard heritagists, including UNESCO and a group of engineers, who insist it can be saved.

The cathedral's fate is still being fought out in New Zealand's Supreme Court. There are people for whom Christchurch is unimaginable without its stone cathedral, which was begun in 1864 as an insanely grandiose project by a settlement with fewer than 1000 inhabitants.

Everything came down in 20 seconds, under the force of one of the most violent vertical shock recorded in a city. A lot of what didn't fall that February 22 in 2011 was brought down later, damaged beyond repair.

The New Zealand Army arrived days after the earthquake to help retrieve the dead, treat the injured, rescue the trapped and provide food, water and electricity to a people suddenly without them. The army stayed until the middle of last year, controlling all access to the city centre and presiding over a progressively shrinking area as the periphery was freed up.

In February 2014, you no longer needed a special permit to enter the centre of the city. You did need determination to get around the deceptively vast areas fenced off with cyclone wire. Making sense of things on the ground in Christchurch is like interpreting the remains of Pergamon or Selinunte. Or feeling how it must have been to arrive in Berlin or Tokyo after World War II.

Fluorescent and hard-hatted, on my second day I followed architect Peter Marshall into the city's Town Hall of the Performing Arts. It's a big, strong building from 1972 that survived the earthquake intact. But its ground floor is now buckled and sloping. The land below its foundations fell away massively toward the river it stands by. It has been decided to remove and replace the foundations below it, bit by bit.

When you look at the size of the building and see the mass of its supporting pillars of reinforced concrete, it looks an impossible job. The Town Hall is not high, but it covers a considerable area, sitting on the ground like a huge, white, stalkless mushroom. But Warren and Mahoney, the Christchurch architectural firm that designed it more than 40 years ago, are confident it can reposition the intact mass on a new foundation.

Inside are the gutted shells of a concert hall and a theatre. Their perfect acoustics were an early achievement of New Zealand's Harold Marshall, the pioneer of moveable panel design and, in his old age, the acoustic designer of the Guangzhou Opera House and the new Philharmonie de Paris.

Other work I saw was weirder to behold. I heard a lot about getting the new Christchurch - and especially its business centre - "up and running". What I saw was the 1908 Theatre Royal being entirely rebuilt in reinforced concrete and slightly different dimensions, to be fitted out with plush upholstery and plaster mouldings that will make it seem exactly like the Edwardian original.

And over at the old neo-Gothic complex of the original University of Canterbury, relays of the world's remaining master artisans in medieval stonemasonry were restoring the buildings of what was and will be the Arts Centre. Stone by stone.

Three years after the earthquake, these were the only things I saw happening on the ground. The rest was still on the computers. There was a lot of it, and a lot of it was being done by Warren and Mahoney (who hosted me and our photographer) in several studios around New Zealand, and in the one they recently opened in Sydney's Surry Hills.

All I saw of the future city was a rapid slide show of artists' impressions of a series of low-slung cuboids. The maximum height allowed for new buildings is 28 metres, seven or eight storeys. Sensible and appealing enough for a modest city of under half a million people, though the rationale of lasting trauma in the city didn't entirely convince as an argument against height.

Warren and Mahoney have long had the biggest architectural practice in Christchurch and they have secured most of the big design jobs in the city's rebuilding. A lot of the office buildings still standing uncertainly in the centre - upended cuboids, not all of them quite vertical now - are their earlier work.

In their abandonment, these do not look like great designs. They display the motifs of jobbing commercial architecture over the decades. Some 1960s brutalism, a lot of the brown aggregate cladding popular in the early '70s. An amusingly redundant faux balcony superstructure from the postmodernist '80s. And so on. You wonder whether the new Christchurch is going to be imprisoned in the stylistic moment of its rebuilding.

Certain moments in style hold great promise. In New Zealand's North Island, the town of Napier that emerged after it was levelled in a 1931 earthquake wasn't much liked at the time, but is recognised now as one of the world's art deco jewels. The present, architecturally speaking, offers mixed possibilities. All I could guess at from the slide show of the new Christchurch was a general modesty of aim.

One new building is finished: the tent-like and much visited transitional cathedral, designed by a Japanese architect with local collaboration. Shigeru Ban, from another earthquake-racked country on the Pacific fault line, specializes in the design of temporary emergency structures in lightweight materials, and his structural use of cardboard tubes in the relief cathedral is highly visible.

It's a very pleasing building with a light-filled and flexible interior - high technology meeting ancient Japanese building craft - let down only by the gaudy panels of mock stained glass that fill the triangular front wall. As a first new building, it's pretty promising. But its Japanese designer is an anomaly among the architects working to rebuild the city.

Talking to the architects at Warren and Mahoney felt more like talking to engineers than to other architects I have known. As the son of an engineer, I recognised the enthusiasms of the practicable, the privileging of the concrete detail, the animal wariness of big abstract words like function, meaning and value. These men - Warren and Mahoney is an overwhelmingly male practice - were happiest describing the layer of rubber they were inserting into the foundation of their new structures, allowing buildings to move with an underground shock and remain stable.

The practicality was bracing. I asked why they weren't remaking the city from scratch, maybe on a new site. They mentioned the substructures that underlay the grid on which the city had been built. The water mains, the power lines, the fibre-optic cables and so on, worth many billions of dollars and still perfectly functional.

Then they pointed out the massive legal consequences of legislating away prior ownership rights, litigation's cost in time and money. The sight of so many weakened buildings still standing was the visible sign of this, as conflicts over repair or demolition dragged through the courts, or waited on a final verdict from Gerry Brownlee, the minister responsible.

Warren and Mahoney were part of the consortium that drew up the city central reconstruction plan called The Blueprint. It was prepared in a hundred days for the Canterbury Earthquake Recovery Authority (CERA) and presented in the middle of 2012. The plan identified 16 "anchor projects" for first building - precincts of civic importance like health, justice, transport, retailing, sport and performing arts.

How would people live in the new Christchurch?

The original settler city began as a vision and a statement, one articulated in Victorian England by a sickly young Tory named John Robert Godley. He was alarmed by his church's decline and England's dangerous slide toward social equality.

Godley joined forces with E.G. Wakefield, an imperial politician who had already left his peculiar stamp on the colony of South Australia and the settlement of Canada. Godley and Wakefield started the Canterbury Association to found a colony and transplant to New Zealand's South Island a cross-section of their ideal English society, including aristocrats and a designated peasantry selected by the Church of England. The first ships arrived in 1850. The settlers' historic task was to regenerate traditional English religion and social hierarchy in the south seas.

The realities of building a city and farming uncultivated terrain soon broke down the old world order. Wakefield followed the settlers to Canterbury three years after the first ships, expecting to be greeted as their visionary leader. The settlers quickly put him right. After a few weeks he decamped to Wellington and never returned.

Keeping outward forms of Englishness if not the social realities, the city was enclosed by four wide avenues in a grid based on the City of London's square mile. Oaks and willows were planted everywhere. Cricket was played. Punts were poled along the river, as at Oxford.

The neo-Gothic stone cathedral took more than 40 years to build. Christ's College, a grandiose, mock-English stone public school, had opened by 1851. The neo-Gothic stone university complex was begun in 1876. Plainer and more handsome civic buildings went up around the grid (the delicate-looking wooden ones turned out to be the toughest).

Such was the torpid and slightly creepy faux-English provincial town I flitted through as a 12-year-old, a century after it began. A statue of Godley, founder of the city he named after his old Oxford college, fell down in the earthquake. Queen Victoria's bronze monument was unmoved.

Half a century after I knew it, Christchurch was in serious decline. At the time of the earthquakes in 2010 and 2011, a third of its office space was vacant. It was a city adrift, an economy in decline. The near total destruction of central Christchurch represented an amazing opportunity for renewal.

I wanted, on the afternoon of my third and last day in Christchurch, to hear from CERA what its vision was of a Christchurch renewed. How would the city be, a century and a half after its beginnings as a colony of Victorian Britain? How did the planners see the city and the region now? How did the city see itself? What did the government want to tell New Zealanders, in making its $40 billion investment in a new city, about their country in the 21st century? How did New Zealand want to be seen by the world?

Don Miskell, a retired Christchurch landscape designer who is now CERA's head of design, seemed nonplussed by my questions. He rattled off a summary of replies received in the city council's "Share An Idea" survey. They showed that people wanted a compact, low-rise and green city - trees and grass, rather than renewable energy - with good public transport, bike paths, arts and sports facilities. He said he'd bought a bike himself a week earlier, and had really enjoyed riding home in the rain the night before.

But what was the New Zealand government saying with its $40 billion? Don Miskell said the government was itself only investing a quarter of this amount. The rest was coming from international insurance interests. He mentioned American investor Warren Buffett. It was my turn to be nonplussed.

People had also said they wanted "high-quality inner-city housing ... a city for all people and cultures ... an urban environment for future generations". I'd tried in vain to get the architects to talk about housing. Ten thousand homes had been destroyed by the earthquake, and the ground under a large suburban area had liquefied and become uninhabitable. All the architects of Warren and Mahoney had wanted to talk about were their public buildings.

But apart from an unbuilt experimental housing precinct on the edge - one of the anchor projects - I saw no inner-city housing marked on the plan. Don Miskell told me that CERA had acquired four large blocks running together down the eastern edge of the city centre, intended for mixed housing and parkland.

The artist's impression showed a long strip of grass and pavement running between two uniform rows of young professional townhouses. The strip between the lines of houses was 40 metres wide - because, Miskell told me, at 20 metres you could still see the look on a person's face. The townhouse occupants would police the strip through their front windows on either side, ensuring it did not become a new terrain for dealers in substances and their clients.

This strategic beautification was a response to the fact that a nearby park had become the domain for illicit trafficking. It recognized that all was not entirely well among the people for whom the new city was being built.

Christchurch has its dark side. Over breakfast each morning, I read progress reports of a case in which a young woman had been tortured to death and thrown into the river by gang members after a dispute over drug payments. Self-policing townhouses didn't seem much of an answer to social malaise.

Nearly 10,000 kilometres to New Zealand's east, in yet another long, thin, earthquake-racked country on the Pacific rim, Chilean architect Alejandro Aravena has built thousands of homes that confound everything you thought you knew about low-cost social housing except their rigorous respect for budget limits. Forget Stalinist monoliths planted on the edge of nowhere. And forget townhouses.

Aravena has built complexes of low-cost housing in city centres in northern Chile, among the homes of the rich. And where the money constraints were too tight, he's built clusters of "half-houses", structures that provided essentials and left space for occupants to add more as their money and imagination might later allow.

He has collaborated with the Catholic Church and the mining and oil industries to create a common good. The social mix, the economic and social tensions built into his urban designs, have released a dynamism into cities that no one, except the architects themselves, had imagined.

A larger social imagination was hard to find in play over my three days in Christchurch. I had the feeling that the new city would be much like the old, only with lower buildings that were less likely to fall down. Given the city's origin in a bold if wacky social experiment, and New Zealand's outstanding history of advanced social practice in the last century, the future looked like being a letdown.