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None proved more stalwart than his fellow Yorkshireman Richard Boyle, the third Earl of Burlington. A decade younger than Kent and of an altogether more introverted personality, Burlington none the less invited Kent to move into Burlington House in London – now the site of the Royal Academy – where he lived with the earl and his family for 30 years. Fired by a determination to redirect British culture along Italian lines, Burlington quickly emerged as the pre-eminent patron of the day, revolutionising national attitudes to painting, opera, architecture, furniture and garden design. As the principal beneficiary of Burlington's largesse, Kent soon demonstrated his rambunctious genius across many of these fields, attracting fame and criticism in equal measure.

One of the first objects in the exhibition is Hogarth's print of 1724 The Bad Taste of the Town which satirises the rage for all things Italian. The foreground shows crowds queuing for productions of Italian opera and commedia dell'arte while the rear is dominated by the gates of Burlington House, surmounted by statues of Raphael and Michelangelo cowering at the feet of a triumphant Kent. The pointed loss of the second letter in the inscription of Kent's surname leaves little doubt as to Hogarth's sentiments.

The diminutive villa that Burlington added to Chiswick House in west London in 1729 represents the apogee of his collaboration with Kent. The design of the external structure was the earl's own work and effectively a love-letter to the 16th-century Italian architect Andrea Palladio. Its geometrically precise classicism stood in polar contrast to the English baroque style that had been perfected by Christopher Wren and his followers.

The design of the richly coloured and gilded interiors was Kent's, and his still more influential contribution was the encompassing park. In his use of naturalistic planting and follies resembling classical temples, he provided the ideal setting for Burlington's Roman fantasy and coined a manner of landscaping that would be imitated the world over.

Kent soon found himself in demand from landowners across Britain, each eager to refashion their homes and gardens. A desire to recapture the Italy that they had encountered on the Grand Tour was one recurring motivation behind these commissions, but there was also a strong political impulse at play. Kent's clients were Whigs: a party that had recently formed its first government and whose members were keen to patronise a new style that they saw as emblematic of a new Britain.

When Prime Minister Robert Walpole decided to build a palatial residence for himself in north Norfolk (Houghton Hall), it was to Kent that he inevitably extended the commission to design the interiors.

While country house projects were in no short supply, Kent's overriding ambition was to apply his talents to buildings of national import. In this he found mixed success. He decorated the state apartments at Kensington Palace, but a spectacular model, included in the exhibition, is all that came of plans to build a palace for Queen Caroline, at Richmond.

At Westminster, he built accommodation for the Horse Guards and the Treasury, as well as a Royal Stable block that was sadly demolished within a century to make way for the National Gallery. But the project that would have been his career's crowning work was also destined not to be. This was a Palladian scheme for a new Parliament building on the Thames, which would have been formed the ultimate monument to Britain's reinvention as a constitutional monarchy.

Kent laboured for seven years on multiple designs for the project, but with the government's coffers drained by war with Spain and Walpole's toppling in 1742, it foundered. The medieval Palace of Westminster received multiple additions over the following century before it succumbed to fire and was replaced by Charles Barry and Augustus Pugin's present building. Its neo-gothic style suggests how far the national taste had moved from Kent's vision of a new Britain.

Design may always be a question of imagining a future that is certain to be superseded, but as this exemplary exhibition attests, no British designer made a bolder claim on posterity than the phenomenal Kent.

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