The British Institution was founded in June 1805 by a group of private subscribers who met in the Thatched House Tavern in London. A committee was formed, and in September of that year it purchased the lease of the former Boydell Shakespeare Gallery building at 52 Pall Mall, with 62 years remaining, for a premium of £4,500 and an annual ground rent of £125. The British Institution opened at the Pall Mall site on 18 January 1806.
The founding "Hereditory Governors" included Sir George Beaumont, 7th Baronet and Charles Long, 1st Baron Farnborough, both of whom had employed the services of the leading dealer and picture-cleaner William Seguier, and were probably responsible for his appointment as "Superintendent". Seguier later became Surveyor of the King's Pictures and when the National Gallery, London was founded in 1824, was appointed as the first Keeper, holding all three positions until his death in 1843, as well as continuing to run his business. Above Seguier the Institution had a Keeper, a role given to a series of engravers. The Superintendent was responsible for organizing and hanging the shows, a role that inevitably gave rise to grumbling and worse from artists – at the Royal Academy a committee was responsible for the hang, which allowed someone else to be blamed, but Seguier had no such opportunity to share the blame. In 1833 John Constable wrote with heavy irony of having received a visit in his studio from "a much greater man than the King—the Duke of Bedford—Lord Westminster—Lord Egremont, or the President of the Royal Academy — "MR SEGUIER"." When in 1832 two pictures by Richard Parkes Bonington, who had been dead only four years, were included in an "Old Masters" exhibition, Constable (who was twenty-six years older than Bonington) wrote that Seguier was "carrying on a Humbugg".
Other founding Governors included George Legge, 3rd Earl of Dartmouth as President, the Marquess of Stafford, Sir Francis Baring, 1st Baronet, William Holwell Carr, John Julius Angerstein, Sir Abraham Hume, 2nd Baronet, Sir Thomas Bernard, 3rd Baronet, and others. They were essentially the same group who were to succeed in persuading the government to found the National Gallery in 1824, and whose gifts to it provided most of the early collection. There was a total group of 125 Governors, Directors and Subscribers, paying sums between 100 guineas (56 of them, 35 at 50g., 11 at 10g.) down to one guinea annually. In 1805 the initial subscribers consisted of "One duke, five marquesses, fourteen earls, two viscounts, nine lords, two bishops, four ladies, seven baronets, twenty-two members of parliament, five clergymen and above fifty private gentlemen, bankers and merchants". The Institution had been discussed with the Royal Academy before it was established, and relations were friendly, at least initially, though later there were to be tensions. The Prince Regent was Patron from the foundation, and loans from the Royal Collection continued throughout the life of the Institution. In 1822 the hereditary nature of the Governors was eased out, as they were becoming far too numerous, and the bottom end of the Subscribership tightened up.
The gallery building had been commissioned in 1788 by the engraver and print publisher John Boydell as a showroom for his Boydell Shakespeare Gallery, a large and financially unsuccessful project for a series of paintings and prints of scenes from works by William Shakespeare. The architect was George Dance the Younger, the then clerk of the city works. The gallery had a monumental, neo-classical stone-built front, and three exhibition rooms on the first floor, with a total of more than 4,000 square feet (370 m2) of wall space for displaying pictures. Boydell ran up large debts in producing his Shakespeare engravings, and obtained an Act of Parliament in 1804 to dispose of the gallery and other property by lottery. The main prize winner, William Tassie, a modeller and maker of replica engraved gems, then sold the gallery property and contents at auction. When the British Institution took possession, they also retained a sculptural group on the façade by Thomas Banks, which had been intended to be used as a monument on Boydell's tomb.