The Woman Hater, Orange Tree Theatre, London

One of the sharpest and most shamelessly enjoyable television plays of recent times rejoiced in the cheeky title Fear of Fanny. It's not about crawling aversion to the female anatomy, though there are aspects that abut (so to speak) on that territory, in that the subject of Brian Fillis's drama is Fanny Cradock, the TV cook who was the drag queen of TV cookery back in the golden era of the 1950s to the 1970s. She was eventually dropped by the BBC for being rude to a member of the public. Poor Fanny. She was ahead of her time. These days, she would be raking it in as one of the judges on The X-Factor, or as Gordon Ramsay.

Why did I get on to the subject of fannies? Oh, yes, because it struck me, watching the witty, more-than-faintly camp treat of a Christmas show at Richmond's Orange Tree Theatre, that Fear of Fanny would also make a perfect title for theatre history's treatment of the author of the play that Sam Walters has so deliciously mounted there.

Known, if at all today, as a novelist and diarist rather than as anyone who ever harboured play-making ambitions, Fanny Burney languishes in the collective Trivial Pursuit sector of the mind for two reasons: she wrote memorably of being chased round Kew Gardens by George III, and she recorded in extraordinary prose the ordeal of undergoing a mastectomy. On the play front, hers is a story of almost unruffled neglect except for a brief flurry in the 1990s when her comedy, A Busy Day, surfaced, for the first time in its 200 years of life, twice in quickish succession, on the second occasion for a short fling with the West End.

Now, after another epic gestation period, her sparky, shrewd comic drama The Woman Hater is brought to birth in a labour of love by Walters, a man with a keen obstetric eye for the yet-unborn of yesteryear. Unlike the snow in the Christmas carol, which is deep and crisp and even, the play is fairly deep, certainly crisp, and deeply uneven.

There's a family tree clarifying the connections between the various characters helpfully printed in the programme. Even so, the exposition at the start seems to combine the tortuous convolutions of the first scene of Shakespeare's Cymbeline (without the amusing tone of sly self-guying) with the brain-knotting dynastic complications of his Wars of the Roses cycle.

As in A Busy Day, which is kick-started by the heroine's return from the East Indies to Georgian London and an 80,000 dowry (and which goes on to make shrew observations about the difference between surface and true manners in a world where the landed have been landed with the nouveaux riches), The Woman Hater explores the consequences of a homecoming from the Tropics. Only here, it's a tangle of presumed and actual paternity, a double-booking of daughters, and a marriage wrongly severed because of mistaken ideas about infidelity that spills out.

Staged with droll verve and an artful mix of period and modern fashions by Walters, the play has comic energy and a tendency to oscillate between melodramatic fervour and camp, tongue-in-cheek effervescence (the gear-changes cleverly masked by the inverted commas Walters wraps round the high-flown scenes).

It also boasts two very funny characters, both of whom are given tip-top portrayals here. There's the woman-hater of the title who, in Clive Francis's delightful performance, is a comic pre-coronary in a tasselled smoking hat, and, best of all, Lady Smatter (played with a divinely vague dottiness by Auriol Smith). She fancies herself to be a muse, a mover and shaker in the literary world, and her mind is a mist of half-remembered poetic quotations and indecisive attributions, which, by the time she utters them, sound like half-baked banality. If she were reviewing The Woman Hater, she would say that "As Prior or was it Cowley, or was it Spenser? so aptly put it, 'better late than never'."

To 2 February (020-8940 3633; www.orangetreetheatre.co.uk)