The sleepy town of Letchworth, England, may have been the first garden city, but it wasn't particularly radical, says Owen Hatherley in his latest Opinion column.

In the exhibition Alternative Letchworth, there is a series of little surveys you can fill out and attach to the wall, in the fashion popular recently in contemporary art galleries and museums. One of them asks if you like any of the following: comfortable clothes, healthy food, fresh air and the outdoors, open-toe sandals, and finally whether your school was co-educational. If you've ticked the "yes" box to at least four then it tells you to consider yourself "a Letchworth crank".

It's a neat little joke about this quietly important little town on the northern edge of London's commuter belt, founded in 1903. This is, as a sign at the railway station tells you, "the first garden city", a project influential the world over in demonstrating that new towns planned in a new way were possible and desirable.

In its first years, Letchworth was famous for more radical kinds of crankery, and it's this that the exhibition explores. Other, more uncomfortable – but equally accurate – tick-boxes could ask: "Are you a vegetarian? Are you a socialist? Do you think men and women are equal? Do you think women should wear corsets and that people should wear hats at all times? Are you comfortable with homosexuality? Do you think that society can be improved through architecture and planning?"

The first Garden City advocated the creation of new towns with neither slums nor privileged districts

Many of those involved with Letchworth in the early days agreed with these much more radical statements, much to the scorn of contemporary commentators such as George Orwell; in some ways, their crankery is our normality – in other ways, it isn't. Alternative Letchworth tells their story, and reflects on it through works by local artists.

The first garden city is derived from the book To-Morrow – the Peaceful Path to Real Reform, by the late Victorian pragmatic crank Ebenezer Howard. It advocated the creation of new towns with neither slums nor privileged districts, laid out in a way that was neither city nor country, and which would be owned and run by their residents.

The second part never really happened – there was little real democratic control of the Garden City Corporations which managed the first, Letchworth, and its successor, Welwyn – but the towns got built and they became popular, and for Howard, achieving that was more than half the battle.

Howard wasn't a designer or architect, and it's perhaps happenstance that his ideas were executed in the golden age of the Arts and Crafts movement, a socialist-inflected attempt to re-create the allegedly fairer, more communal life of the middle ages. Raymond Unwin and Barry Parker, the planner-architects of Letchworth – and of its derivatives, like Wythenshawe in Manchester – were committed socialists and committed medievalists. They insisted on organic materials, romantic aesthetics and extremely low densities. In To-Morrow, Howard imagined a circular "crystal palace" around the edge of the centre of garden city, but that sort of futurism wouldn't creep into new towns until the 1960s.

Letchworth is an odd idea of a "city"

Letchworth is an odd idea of a "city". The housing is sleepy, leafy and very pleasant indeed, but the centre is baffling; a high street with plenty of independent shops gives way to a huge, useless, barren square, ineptly lined by pompous architecture of various eras – Neo-Georgian, modernist, Pomo – none of which have anything like the presence or scale to command this vast space. Parker and Unwin and their ilk could plan lovely suburbs, but were clueless in creating urbanity. A welcome hint of the relatively unusual can still be found if you look hard enough – the People's House (derelict), the Brotherhood Hall, the Vasanta Hall of the Theosophical Hall (opposite the Gurdwara), perhaps belying the visual impression of deep English conservatism. But there is one little trace of the "crystal palaces" – the spacious iron and glass Arcade, in which you'll find the Broadway Gallery, which is where the exhibition can be found, just up the stairs near to the sweet shop.

The historical part of the exhibition is great fun, focusing on the feminists, socialists, pacifists, vegetarians and theosophists who made up a vociferous minority of early inhabitants. Even there, they were gently ridiculed in the local press, though the fact that many of their views are now almost totally accepted (or at least, lip service is paid to them) is a reminder that "normality" makes little sense viewed from a historical perspective.

What may be harder to recapture is the belief of the founders in the social powers of design, and that's where the newly commissioned work comes in. Chantelle Stephenson's sculpture derives from The Cloisters, a school and social centre on the outskirts of town more spatially radical than the polite single-family houses that define Letchworth. Sean Pearce's photo series Paint Me in a Nice Light focuses on a post-war council estate within the garden city, feeling slightly desolate and disconnected from the preserved closes of Parker and Unwin; a sign in front of the houses and open spaces reads PAINT ME. John Vincent's The Last of Letchworth is a hallucinatory film in which a toga-wearing figure limps through the garden city; and Jane Fae's contribution is a book charting the gradual watering-down of the original egalitarian ideas of the town.

The British government likes to talk about building new garden cities, but never about building new new towns

In all of these, you can get the sense that the hope and the reality never quite met, as Letchworth became just another affluent Hertfordshire commuter town. As the planner and writer Adrian Jones puts it, "Letchworth is a comfortable place in an increasingly uncomfortable country, and that is why people like it". That isn't to be sniffed at, but it would have disappointed the radicals of the 1910s.

Another tick-box at the end asks: "Do you think Letchworth Garden City is socially conservative or radical?". William, 72, has ticked "conservative", and added "too interested in their property". The Garden City Corporation – now the Heritage Foundation – is still important, and the city is clearly proud of its legacy, which isn't always the case with the new towns that borrowed from it after 1945. But the best of them achieved something Letchworth never did – some architectural urbanity, and some measure of real social progress, with hundreds of thousands of people moving from the slums to live the garden city dream of rangy houses in abundant open space.

With little state support, the original garden city became reliant on an uneasy mix of private finance and local enthusiasm; the main employer in a town where women who didn't want to wear corsets could feel comfortable became the Spirella Corset Factory.

The British government likes to talk about building new garden cities, but never about building new new towns, which are still associated with unfashionable concepts like modernity, public ownership, and equality. It's this, rather than a love for alternative lifestyles or Arts and Crafts architecture, that has inflated the reputation of the garden cities.

At the railway station is an advertisement for Le Jardin, Luxury Retirement Living, a "stunning collection" of one- and two-bedroom retirement apartments. Its architecture is a debased version of Parker and Unwin's asymmetrical, pitched-roof style, with none of the space or grace. That's where utopia ends, here.