The city's new theatre marks the end of an era of exotic public building for the cultural good. And it's one more reason to visit, says Nick Coleman

So, this Archbishop walks into the bar in the upper circle, gladhands a ruck of civic dignitaries plus the odd actress, tells a funny story, and then, with fitting solemnity, blesses the theatre.

It sounds like the beginning of the sort of joke churchmen are wont to tell each other over sherry – the sort that ends with the punchline, "but then, this is the Church of England".

But it isn't a joke. The Archbishop of Canterbury really did walk into the most dramatic new building erected in his episcopal city since the 11th century and he did, indeed, press flesh, make a speech and bless the building. And he did make everyone present laugh, by explaining how, on this, the feast day of St Ninian (16 September), it was only appropriate that he should be praying on behalf of a brand new theatre. St Ninian was, you see, "the Apostle to the Southern Picts" – and everybody knows that the Picts got their name because they were "painted people".

In the absence of a drummer to execute a quick press-roll and crash on a cymbal, Dr Rowan Williams then dropped his remarkable eyebrows with perfect comic timing, which had more or less the same effect. He's a natural.

But the gags stopped there. The Archbishop also had some serious observations to make. The man with the second-most undoable job in national life (after the England football manager) didn't get where he is today without seeing where the essential matter lies. In the case before him the essential matter lay not within the pre-oxidised copper sheeting and Spanish dolomite aggregate facings of the Marlowe Theatre, but in what that structure stands for. "The flourishing of British theatre is still one of the most exciting things about British society," he said, sonorously, and then continued with careful emphasis: "In its way – in its way – [culture] is as important to the community as jobs and the local economy." He talked cogently about food for the spirit and concluded, with archiepiscopal firmness, that the "flair" (or was it "flare"?) exhibited by the Marlowe's architecture was a beacon.

Canterbury City Council, which took the biggest risk with the project, will be praying that the Marlowe flair/flare will, indeed, set a fire in the minds of all who think inquiringly about Canterbury, and quickly. It is, after all, virtually the last of its kind. Over the coming years there will be precious few outbreaks of either form of the "fl-word" in the cultural-architectural life of the nation. Not anywhere. For, surely, the recent era of exotic public building for the benefit of the cultural good (see also Margate, Colchester, Gateshead, Walsall) is irremediably a thing of the past, Lottery or no Lottery. The Marlowe was itself funded in large part by the City Council, in a somewhat unbalanced public/private deal, and not without the odd raised eyebrow along the way.

So we'd better enjoy it, not least in the terms in which it was designed to be enjoyed: not as the last of its kind, but as an exemplar of its kind.

How will the city benefit (beyond the obvious boon from a newly speeded up railway connection to London, allowing audiences to get back to the capital after a show)? The new Marlowe raises capacity to 1,200 and cushions those bums in orange Italian leather, reconfiguring the seating so that even the most distant audient feels close enough to see the fuzz on a diva's forearm. There is real tension, too, architecturally speaking, in the forms within the space: the origami ceiling, the bent Spartan bow described by the line of the circle, the sense of poised functionality.... Dark wood may not be to your taste but, as provincial theatre auditoriums go, the Marlowe's looks absolutely first rate. Canterbury now has a theatre to rank, in commercial terms, with those in Norwich, Plymouth and Newcastle. Aesthetically, it outranks them.

So what does go through our heads when we think inquiringly about Canterbury? And why was it necessary to spend that £25m? What is all that money being required to enhance?

After all, Canterbury is not profuse in our imaginations, but it is deep. It sits there in its key position on the road from the immigrant Kentish shore, a convenient one-stop pillaging point en route to the capital, prey to the appetites of passing Romans, Christians, Saxons, Jutes, Vikings, Normans, Peasants and Heinkels – it was bombed as part of the notorious "Baedecker Blitz" during the war, in reprisal for the RAF's devastation of Lübeck. All things considered, it's a miracle that this most Sellar-and-Yeatmanesque of English cities is still standing, let alone building on its myth.

There isn't much of it for a start, and most (but not all) of the attractive bits are enclosed within a flinty Roman wall and the obligatory ring road: an interior Canterbury bejewelled by the cathedral which provides Dr Williams with his seat and is the shrine to the martyr, Beckett, who lost the top of his head there in 1170. That's why people make pilgrimages to Canterbury: Beckett and Chaucer. It's the place where we expect to connect with the depth of our Englishness.

That is certainly the sense conveyed by Powell and Pressburger's lovely-but-bonkers A Canterbury Tale, the wartime propaganda film which elided the 14th century with the Second World War in an early cinematic blitz of psychogeography. Canterbury is a properly iconic city. In our minds, at least, it ought to be the nearest thing we have in city form to Blake's Jerusalem. But, of course, it's nothing like that all.

I am to be escorted around the premises by David Kincaid, the local council's Principal Conservation Officer. He likes bricks. And tiles and flint. Not to mention ragstone. Wattle and daub too, probably. He is certainly affronted by the "pigeon crap" which Jackson Pollocks the waterside half-timbering of the Old Weavers' House in High Street – he doesn't say as much but it's clear that he regards pigeons as the lowest of the low. Visigoths with feathers. David is a man born to the fabric of the world and he makes a fascinating guide to the streets, walls, buttresses and gateposts of the city.

Most guides would kick off a walking tour on the main medieval shopping drag by pointing out the city's greatest hits. You know, the cathedral, Debenhams, the museum. Not David. He introduces me to a medieval wall in an Italian restaurant (it's two feet thick and marvellous) and then immediately heads off down a quiet side street to show me some particularly interesting bricks.

It's called Stour Street, this delicate artery, and if you know how to look, it is the filament which reveals the truth about Canterbury's varied fabric – a metaphor for something, surely. There are "mathematical" tiles pretending to be bricks, from that period when bricks were considered sexier than tiles, but tiles were cheaper. There are bricks fired in one way so that they have acne, in another way so they don't. The acne was caused by "London rubbish" brought down the river from the smoke as ballast and introduced to the clay. The rubbish caused the bricks to fire at a higher temperature with the result that the bricks are yellow and the acne blue.

There is also the rather lovely, low, flint-peppered structure of the Poor Priests' Hospital, which currently serves as the Canterbury Museum and the repository of all things Noggin the Nog and Rupert Bear (Oliver Postgate and Mary Tourtel were both local luminaries). Further on, there is what remains of the vast tannery, which was heavily whacked by the Luftwaffe and is now being converted into housing. The pong of the tannery may have gone, but the "slub" by-product of tanning – a glutinous emulsion of fat, hair, dung, urine, salt and water – provides a resistant underlay to the nearby ring road and adjoining field. The ring road is holding up well.

At the bottom of Stour Street, after it gives into Church Lane, close to the wall, the ancient church of St Mildred's tells a variant of the same story. The Saxons who built it and the Normans who repaired it were heterodox to the hilt in their use of materials. They'd build a church out of any old crap lying around. And so it is salutary to learn that lovely, solid St Mildred's is, in fact, a collage of Roman brick, Caen limestone, ancient flint, ragstone and, for all we know, Jute slub. In Canterbury, it seems, anything can be built out of anything.

Or put to any use. For instance, the Norman castle keep, located within easy trebuchet range of St Mildred's, served for much of the 19th century as a coal bunker, the coke being piped in a continuous stream from an outlet in the bottom of the ramparts to the Gas Light and Coke Company over the road. Think about it. An 11th-century motte full to the brim with crunchy 19th-century industrial fuel. How unanswerably resonant is that?

While in Canterbury, you should visit Debenhams, to buy stuff if you must, but more importantly to see the exposed inner structure of a 14th-century house, all gnarly and raw on the staircase and first floor, as if jerkined men with adzes have just finished sucking their teeth over it.

I could go on.

But I want to duck the cathedral and Greyfriars and Whitefriars and the Beaney art project (due to open next spring) and the Sun Hotel (Dickens) and Westgate Towers (nice new café) and get back to the Marlowe, because that's where Canterbury finds its brightest heterodoxy.

"Suitably protean ... collage architecture," The Independent's critic called it, which is an allusion to the slippy-slidiness of the building's visual impact and its multi-layered architectural provenance. The eye travels over it; the mind wishes to enter. It is the opposite of a monolith. It is fronted by a socking great colonnade and topped out by a mesh-coated triangular flytower, which "disappears" in certain meteorological conditions. But, otherwise, it defers to the cathedral's ownership of the skyline. The building's surface is white, grey, oxide-brown, black, silverish. It looks like a mechanism requiring only the touch of a button for its highly visible works to start gyring inside, prior to ... what? Lift off? From the interior, its glass frames some of the most magnificent elevations of an Anglican shrine you could wish for.

Powell and Pressburger's funny, idiosyncratic, romantic Canterbury Tale stretches Chaucer and the historical idea of the pilgrimage to represent a model of social, national and, ultimately, international cohesion. To make that stretch, it rolls out a barmy narrative metaphor involving wishfulness, questionable identity, railways and glue – and the story ends in rejoicing. Clearly, things haven't changed all that much in Canterbury.

Compact Facts

Further Information

Marlowe Theatre (01227 787787;