Burlington House was one of the first three mansions built by the area that would go on to be known as Piccadilly Circus. Construction began in 1665, designed and paid for by Sir John Denham, the poet and Surveyor General of Works. Denham would sell the property two years later, before the house was completed. The largest factors leading to Denham selling the property was the passing of his wife and his own failing health. Some remnants of Denham's original building can still be seen in the current structure.
The property, which became known as Burlington House when the Earl of Burlington purchased it from Denham, changed hands over the ensuing years until the British government acquired it in 1854. Under the government, Burlington House became the headquarters for a number of scientific advisory boards, most notably the Royal Society of London (for Improving Natural Knowledge).
The Royal Society was founded in 1660 as an assemblage of natural scientists who met weekly to discuss experiments and the promotion of the natural world. The British government began paying them a stipend of £1000 a week in 1850, which began a close relationship that lead to the Royal Society being granted a home in Burlington House.
The Society's motto is "Nullius in verba" - which basically means, "Take nobody's word for it." A motto to live by.