Note: The table retains the original handles and castors. The original rising ratchet mechanism is fitted with a faded green leather insert of later date.
The Carlton House style of writing table was made fashionable by the Prince Regent , later George IV, in the last decade of the 18th century. Carlton House, the official seat of the Prince Regent, was lavishly furnished by several leading London cabinet-making firms including Gillows, who supplied the large table and chairs for the dining room.
The cabinet-maker John Kerr of Pall Mall supplied one mahogany and one satinwood writing table in 1796 to Carlton House for £22 1s 0d and £16 9s 0d respectively.
Kerr also supplied this type of table to the Duke of Bedford at Woburn Abbey.
These were not the first writing tables of this design, however. The design was first published by George Hepplewhite in 1792, and was also used in The Cabinet-Makers' London Book of Prices in 1793, where it is signed Hepplewhite and dated 5 October 1792.  (Intriguingly, however, it does not feature in any of the three editions of the book of designs, published by his widow Alice after his death.) 
The design was also copied by Thomas Sheraton, who published it in The Cabinet-Maker's and Upholsterer's Drawing Book in 1804. The plate is signed T. Sheraton and dated January 16th 1793.
Gillows supplied such a table to the Earl of Derby in 1798.
We will probably never know who invented this type of writing table, but it was undoubtedly the tables made by John Kerr for the Prince Regent that led to the style being known by its now familiar name.
Gillows used the term 'Carleton House Table' as early as 1796. A sketch for the table in their cost book of that year states that a Mr. Becket made the piece for Gillows of London at a cost of £17 8s 8d.