Visitors once travelled to this provincial town for the waters. These days, they come for the festivals. Nick Coleman seeks intellectual refreshment

'This town," says Donna Renney, marching purposefully up to the front door of the Hotel du Vin, "was built on pleasure. It is, for want of a better expression, a pleasure town."

The Hotel du Vin in the Montpellier district of Cheltenham is a sort of pleasure hub. It is where all those jazzers, classical musicians, authors and science boffins convene for after-hours pleasure following a strenuous stint providing entertainment for the teeming multitudes at Cheltenham's four annual festivals – festivals which set the standard for salubrious culture in high-end surroundings (and serve as a counterweight to the town's other premium festive product, horse racing).

It's a nice joint, the hotel. Even now, in between festivals, you can see how it all might work in here while the festivals are on: literati jabbering on the bar banquettes, saxophonists trilling late-night standards in the downstairs restaurant area, mezzo-sopranos not straining their voices over brandies in the foyer, scientists enjoying themselves in the outdoors area with clipboards. The temptation in Cheltenham is always to follow the line of the pointing finger and go: "Coo, posh!"

Posh? Well, sort of. Not posh as in aristocratic or even in David Cameron's entitled-upper-middle-class metropolitan-sophisticate sense. But posh as in nice, quiet, comfortable, cultured, well-heeled, thoughtful, sensitive, enfranchised, responsible, endowed, endowing and genteel. Posh as in "wouldn't we all settle for a little of this, if only we could?". Posh as in the total absence of the not-so-nice.

But then Cheltenham was built on a certain kind of pleasure. It exists in its present, predominantly 200-year-old, form as a place devoted to making people feel good in themselves. It has a little light industry (landing gear for aeroplanes, environmental science, insurance, spying – that sort of thing) but nothing that's going literally to soil the hands. It is a Regency spa town, with working waters, and with one serious rival for 18th-century handsomeness (the even more architecturally spectacular Bath). It has no serious rival as a provincial festival town. Yes, there's Edinburgh, I suppose, but Edinburgh is a festival monolith. And you can argue that Hay-on-Wye gets a proportionately greater deal of attention for its literary festival. No question, Hay has its vibe. But you should hear Donna Renney on the subject.

"Yes, well, we position ourselves very differently to Hay," she says. "The Glastonbury experience is not for us. We have pavements, not fields."

Renney is the chief executive of Cheltenham Festivals, an imposing, amiable, linen-clad woman of irresistible enthusiasm. She is taking a day out of her busy schedule to show me round her home town with a view to demonstrating that my prejudice regarding Cheltenham – namely that it is the sine qua non of smug embourgeoisification – is nothing but a misconception. Or words to that effect.

We've got on extremely well so far. We've clumped out of Montpellier and up The Promenade, which is spacious, airy, verdant and surprisingly continental. There's a well-turned-out farmers' market down one side, masking the façades of local government offices while, down the other side, the usual phalanx of the classier sort of retail outlets do their discreet thing. Up the middle are pavements, trees and statuary (well, a statue, of a minotaur and a hare) and ambling white people looking cool and soigné in the mid-June heat. The cheesecake ambiency of all those creamy Palladian shopfronts is soothing. Even the occasional modernist office block is finished in elegant Bath stone. In keeping.

"Yes, the ladies who lunch and the tweeds – to some extent that's true of Cheltenham." Donna is warming to her theme. "That is inescapable. But next year we intend to have even more space and to do more. We are very fortunate to have the power of four." This is said with a modest flourish. "Ours is the only festival city where all four festivals are under unified control, and that gives us so many more opportunities to do so much more." She fixes me with a beady, not unironical eye. "I like to think of Cheltenham as a spa for the mind, as a place for intellectual refreshment."

I laugh, and so does she, thankfully.

In due course, we descend upon Imperial Square Gardens, a large green space broadly quilted with chintzy flowerbeds and, in those areas where the flowerbeds aren't, yellowing rectangles of traumatised grass. This is Festival Central, the public space where for a goodly portion of the year marquees are pitched. Pleasure Pavilions, I suppose you might call them.

"Hmm. We've got a bit of a battle on with the council," says Renney. "See those flowerbeds?"

"Yes. Ornamental!"

"Well, quite. They look pretty I suppose, but they do take up rather a lot of space that might be put to more, um, creative use. If they weren't there, we'd be in a position to rotate the sites of the marquees to give the grass a chance." Donna hitches her bag on her shoulder and sighs. "The flowerbeds are also vulnerable to trampling."

This is not said threateningly, but one does fear for the future well-being of the pansies.

We stand behind the Town Hall while the chief exec outlines her vision for the "glass and steel" structural augmentation that would, in her mind's eye, enhance the flexibility and sheer aesthetic appeal of the building, were it to be added on to the rear elevation. Renney sketches the architecture in the air and it is almost possible to see it there for a moment, shimmering. And then, indoors, we stalk the corridors, while I admire the space, the acoustics, the usability, the sheer townhalliness of the Town Hall in all its century-old Edwardian pomp. The main auditorium is compared to "the inside of a wedding cake" and it is not hard to see what is meant by this.

So far, so embourgeoisified. But I am not the first Roundhead spirit to take issue with Chelters, not by a long chalk. As far back as 1825, the great reformist William Cobbett was railing against the sheer frightfulness to be witnessed upon the boulevards of the town. Although it wasn't the bourgeoisification that got his goat. Oh no. Back then, the population of 20,000 nearly doubled "in season", as every Tom, Dick and sozzled Harry would roll into town as if it were Newquay in July and surf's up. "Half clown, half cockney," Cobbett spluttered. A resort "of the lame and lazy, the gourmandising and guzzling". Cheltenham has not always been prim.

Then there was the Reverend Francis Close, the ultra-evangelistic rector of St Mary and St Matthew throughout a hefty chunk of the 19th century, who adopted a moral position in life that was basically, and four-squarely, against pleasure. Close rose to great eminence in the town and endowed it with all kinds of benefices to enlighten the poor. He was a good man: it was what he did. Indeed, Close was the reason, according to Donna Renney, that the railway service from London to Cheltenham is still so slow and awkward (a victim of Rev Close's isolationism and then, 100 years later, Dr Beeching's depredations). Close was the reason the town has in the past been gripped by the fever of Temperance. He is the reason there remains a strong evangelistic tradition in Cheltenham. Where there is pleasure in abundance – and racecourses – there shalt thou also often find people not having fun, and enjoying it. Tennyson called Close "the Pope of Cheltenham", which must have really pissed him off.

Still, it's hard on such a sunny day to feel much sympathy for him, however round one's head. And through the course of the afternoon's gallumphing around I am gradually lulled into enjoying the town for what it is: civic cheesecake on a saucer of cultural cream.

Take the Pitville Pump Room, perhaps Cheltenham's most-photographed aspect; what Donna describes as "a pleasure dome". Now there's a building of supremely fatuous splendour. Fatuous because it isn't designed to do much other than frame the narcissism of those who like to mince around publicly in expensive clothes; splendid because ... well, because it is. And don't try telling me that this extraordinary neo-Classical edifice was put up on the outskirts of town for the health of the poor and needy. The poor and needy don't need to drink stinky water out of nine-foot marble dispensers while everybody watches. They can do that at home, out of buckets.

Because pleasure is, of course, a privilege – or at least the control of it is. And it is in the leafy purlieus of Montpellier again that one can sneak, with permission, into a building which enshrines both the privilege of pleasure and the pleasures of privilege.

The Parabola Arts Centre is a new theatre and arts complex built by the benefactors of Cheltenham Ladies' College for the primary benefit of those eponymous teenage ladies. The Parabola has ancillary rehearsal spaces, offices and art gallery. It appears to be air-conditioned. It is without doubt the most beautiful school theatre I have ever seen, and I've seen a few: perfectly proportioned, brilliantly equipped, tastefully apparelled and obviously built to an astonishing level of quality. But then it did cost £12m to put it there, all told. Mostly old girls' money.

And perhaps we should take it as a sign that privilege in Cheltenham is not entirely ring-fenced to benefit the lucky few that, for 18 out-of-term weeks in the year, the Parabola is available to non-College creative enterprises to make of it what they will. The chief executive of Cheltenham Festivals is all over it like a rash and ordinary paying patrons are now also privileged with the opportunity to point their fingers and gasp: "Coo, posh!" You can do it yourself this very month, if you feel like it.

Funny place, Cheltenham. In fact, if you haven't paid a visit, I'd hazard a guess that you'd think it's not quite like anywhere you've ever been before. It is truly, virtuously provincial in a way that neither Cambridge nor Oxford can claim, with their increasing burden of London commuters. It is not in the least bit groovy, which puts further distance between it and its simpering Regency twin, Bath. It is holding up pretty well as a looker, which is more than can be said for any number of tragically withered "heritage" towns and cities up and down the country, buckling under their own burdens of gruesome high street homogenisation. And there really is something to go there for, other than its fatuous splendours.

You've missed Jazz and Science but Cheltenham Music Festival runs until 17 July. The Literature Festival is in October, pavements and all. Yes, it is a bit tweedy and genteel, Cheltenham Spa, but it is also an artistic power shower for jaded sensibilities. At least, I think that's how Donna Renney put it.

Compact Facts

Further information

HSBC Cheltenham Music Festival runs until 17 July. For more information about this and other events, go to cheltenhamfestivals.com

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