I have a friend who changed her name between school and university from Debbie to Natasha. She didn't feel like a Debbie, she said. Inside Debbie, it seemed, there was a Natasha just begging to get out. And she was right. Like a transsexual man who has always known they needed to be a woman, Debbie made a much better Natasha than she ever did a Debbie. She had the hair for it. And a lot of handkerchiefs embroidered with the letter N.

Names are much more than mere labels. They are statements of intent. Likewise the use of the owner's name for the title of their restaurant can be a clear and precise way of defining a business. You'd know what to expect from a place called, say, Darren's or Kevin's - I think it would have something to do with fried onion rings, Blue Nun and a punch-up just after last orders. (This is because I'm an outrageous snob.) The best example of this at the moment is a fine restaurant in South London called Chez Bruce, which to me speaks of a perfect balance between French precision and Australian informality. That pretty much describes the place.

You would also know what to expect from a place called Jeremy's, wouldn't you - something comfortable, light, stylish without being overly ambitious, maybe a little fey, a little chintzy around the edges. That just about sums up Jeremy's at Borde Hill, chef Jeremy Ashpool's restaurant set in one of the old buildings on the Borde Hill Garden estate just outside Hayward's Heath in Sussex. A light, airy room decorated in shades of deep blue and peach looks out over a Victorian walled garden, currently playing host to an exhibition of sculpture for sale.

Elsewhere on the estate are formal gardens, an adventure playground for kids and a Tudor mansion house - all of which the diners gain free entrance to. There's also a smallish garden centre. I've had very bad experiences of food around garden centres in the recent past. To me, a garden centre near a restaurant is like a lighthouse to a mariner: a warning to steer clear.

Happily, we didn't. It's not that Jeremy's is without faults. Tasters of tomatoes stuffed with a curried seafood mousse were the sort of underwhelming canapé you would get at an overly ambitious Berkshire wedding. (I told you I was a snob.) And my starter of seared tuna with a niçoise-style salad and anchovy mayonnaise was a bit of a mess; the dressing underpowered, the salad a poor assembly of peppers and over-boiled egg. It was not an improvement on a standard niçoise. But these failings are far smaller than its successes. Jeremy Ashpool uses lots of local produce, and he uses it intelligently, in a way that reflects the abundant greenery beyond the windows.

One of the reasons I am so enamoured of the place was that they were so comfortable with our son Eddie. They laid on a highchair. They did not flinch when he threw the cutlery on to the floor for the third time. They took him on a tour of the kitchens. To be honest, I think they were more comfortable with him being there than we were. I make a conscious point of taking the boy wonder to restaurants because I do not think children should be excluded. But this time, surrounded by lots of pressed linen and shimmering glassware, I felt we'd overstepped the mark. The staff clearly did not agree. They like having babies around; that is not something you can fake for the sake of good service.

While Eddie threw around lumps of bread and cheese, my wife Pat dug into her starter of carpaccio of beef. It came with a sprinkling of basil, good, salty Parmesan and lots of crisp bean sprouts and chopped leeks which worked beautifully against the softness of the beef. For my main course, I had grilled champ of milk lamb at £15. It was spring on a plate, the perfectly cooked young meat accompanied by lots of baby spinach and new potatoes and small, caramelised red onions. There was something very straightforward about this unpretentious dish. It was all so very Jeremy.

Pat's main course of red mullet at £16.50 also came with many of the same vegetables (and why not? If they're good and in season, they should be used), as well as some huge, tempura-ed capers which were a bit much by themselves but grand alongside the fish. A little dish of saffron risotto turned up late with many apologies and boasting the kind of extreme heat usually only obtained with a swift burst of the microwave. It was a nice enough risotto - once it had cooled down - but, to be honest, not really necessary.

Eddie moved on to his grapes and we moved on to our puddings, which were of the 'fuel for long country walks' variety. A sticky toffee pudding was dark and lush, a chocolate brioche and butter pudding with crème frache equally so. We were both sharing driving duties so, apart from a fine kir, we neither of us did any damage to the wine list, but it is an extremely well thought-out document from both the New and Old World. There's a fair selection of halves, lots of bottles well below £20, and none getting too far beyond that psychologically important barrier, either.

It has a loyal local clientele, and I can see why. If I lived nearby, I would come here often; on a warm summer's evening, dinner on the terrace at Jeremy's must be an exquisite experience. The owner should simply give thanks that his parents didn't call him Melvin. That wouldn't have worked at all.

• Jeremy's at Borde Hill, Balcombe Road, Hayward's Heath, West Sussex (01444 441 102). Dinner for two, with wine and service, costs £80