Piccadilly, London W1 (020 730 5608). Meal for two, including wine and service: £95
Tim Zagat, co-founder of the crowd-sourced restaurant guides which carry his name, told me during a night tour of New York's establishments that he could work out how a place was doing just by looking through the door. He told me a lot of things during what turned out to be a very peculiar evening, roaming dining rooms without eating; sticking our noses into private spaces to see what was going on. Zagat insisted he was keeping abreast of the scene, though as the guides are published in many cities and he obviously can't do it in all of them, it did seem a little odd. Perhaps he just liked being acknowledged by maître d's. I filed his claim of instant restaurant health diagnosis under the heading marked "utter cobblers".
And then I walked into the restaurant at the Royal Academy on London's Piccadilly, and Zagat's claim immediately made sense: here was a space, apparently tucked away as if an afterthought, that was so obviously at ease with itself. Witness: the cultured English middle classes at rest. Everything about the room – the broad vaulting arches, the wood panelling, the red upholstery, the geometric lampshades overhead and, most of all, the casually placed art – is classy without being overstated. Sculptures by great RA names, some in bronze, others in marble or terracotta, are displayed in glass cases stacked satisfyingly one atop the other, so that you look over their curves and folds to the other side of the room.
And then there are the murals: Harold Speed's Autumn, dating from 1898, or Leonard Rosoman's sweet vista, from 1986, of the art crowd flowing up and down the RA's stairs like a river in flood.
Here then, we come to sit, with the annual Summer Exhibition outside the door, and a list of good things to eat in front of us. Not long ago the restaurant was taken over by Oliver Peyton, who has a sentimental attachment to the notion of putting quality places into a city's landmarks, as if it's what London deserves. The Atlantic Bar and Grill was garish and noisy and shameless and exactly what was needed so close to Piccadilly Circus; Inn the Park was what we wanted for St James's Park; ditto the restaurant at Somerset House. A grand space requires a good kitchen. For the most part the RA gets one.
The food looks like the greatest hits from the kind of glossy cook books the people who come here would fill their shelves with. So it's butch and modern and English in places, because we are proud now of our re-engineered culinary heritage, but there are also continental flourishes. There is gazpacho. There is a touch of pasta. A ham hock and crackling salad, bolstered with mustardy strands of celeriac, is a lot of piggy bits in all the right places. Another salad of heritage tomatoes with burrata, the foetal version of mozzarella, is exactly the kind of thing ladies who want to have lunch without really eating would enjoy.
A whole lemon sole, expertly trimmed, seared in butter to the point where its pearly flesh slips from the bone like Venus losing her silken slip (come on, people; I'm in an art gallery) is served with sweet brown shrimps and a beurre noisette. The pecorino filling in a plate of ravioli dressed with truffle oil could do with a little citrus zest to cut through the richness, but the pasta is very good indeed. There are sides of pickled wild mushrooms which aren't mostly shiitake, as is often the case, and tiny roasted new potatoes which we don't manage to finish.
Alongside the sculptures is a display case full of gloriously over-iced cakes, there to signify the commitment to afternoon tea, and they draw the eye as much as do the chiselled and sanded works in marble. Peyton and Byrne bakeries-cum-cafés scattered across London have made a virtue of high-end cakes in places which need them, like St Pancras station or the British Library, so we expected much from this end of the meal. A toffee-and-apple tartlet was not quite enough toffee; a sherry trifle a little too much custard. But these feel like niggles when there is so much quiet (self-) satisfaction to be had from this room, as even the most self-absorbed New Yorker would immediately recognise. It is a place where ladies of a certain age can sit, wearing hats. It is a place in which to stop the world. The slight failings of a mere trifle should not get in the way of that.
Email Jay at jay.rayner@observer.co.uk or visit theguardian.com/profile/jayrayner for all his reviews in one place