WCXX

In his architecture, Kent is usually classed as a Palladian. And his buildings certainly owe a lot to the 16th-century Italian, particularly Chiswick House, inspired by Palladio's Villa La Rotonda near Vicenza. But he is no mere pastiche artist – and his buildings shift comfortably between Palladian exteriors and baroque interiors. On the outside of Horse Guards and Worcester Lodge, Badminton, there is an exhilarating vigour and movement, with the horizontal and vertical stone planes leaping in and out, up and down. His internal architecture is even more` thrillingly mobile. At Houghton, the Stone Hall is exactly that – a hall made of plain stone. But what a riot of stone it is, with its mammoth fireplace and playful pediments. At Kensington Palace, he pulled off a thrillingly vulgar chink of gilded bling for his new Hanoverian boss. His internal pièce de résistance survives at 44 Berkeley Square – where the double staircase flies up, around and across the hall, apparently suspended in thin air.

You've got to be careful about comparing our architects to the best Italian Renaissance and baroque architects. As John Betjeman said, perhaps it's best not to call Weymouth the Naples of Dorset – how many Italians call Naples the Weymouth of Italy? Even so, Kent took the best Italian precedents and altered them in an original way – not least at Chiswick House where, with his patron and co-architect, Lord Burlington, he introduced lines of prominent chimneys to accommodate our unfriendly northern climate.

It seems unfair that Kent was mocked by the fashionable critics of the early 18th century for his supposed dull classicism. William Hogarth – who loathed classicism – labelled him in a picture, The Bad Taste of the Town, as "KNT". The double entendre meant the same thing then, too.

The criticism seems particularly unfair because Kent was no obsessive classicist. As the show confirms, he was adept at Gothic, too, in his designs for Esher Place, and in drawings of Gothic screens at Gloucester Cathedral and Westminster Hall, and a pulpit at York Minster.

When it came to his classical work, Kent wasn't one of those cowboy Georgian builders who flung up a portico and a pediment and thought his work was done. A yearning to innovate and a desire for brio and movement ran through his buildings and his interiors. The funniest, most alluring thing in the V&A is a 1732 console table from Chiswick that is a brilliant little skit on a Corinthian capital.

Even Kent's critics admitted he was on to something with his garden designs. Horace Walpole said of Kent that he was "a painter, an architect and the father of modern gardening. In the first character he was below mediocrity; in the second, he was a restorer of the science; in the last, an original, and the inventor of an art that realises painting and improves nature."

Kent wasn't much of a painter in oils, as his paintings at the V&A show. But, when he used the landscape as his canvas, he approached genius. At Rousham in Oxfordshire, which survives today, he scattered the apparently wild – though actually carefully designed – park with follies, ponds, cascades and bridges. The English Garden look took off across Europe – particularly in Germany – in the 18th century, and it lives on today, wherever there's a touch of asymmetry, or planned disorder, as opposed to the regimented, close-cropped parterres of the Continent.

It's hard to represent gardens in a gallery – though the V&A does its best through drawings, a video and an elegant garden bench from Rousham. Best to visit this illuminating show or read the handsome book, and then to go and see the gardens, buildings and interiors in the flesh. Then Kent – the Renaissance man, Palladian man and baroque man – comes to life.

'William Kent', edited by Susan Weber (Yale), is available to order from Telegraph Books (books.telegraph.co.uk); 'William Kent: Designing Georgian Britain' is at the V&A until July 13