This is the National Gallery, which is situated on the north side of London's Trafalgar Square. The gallery was established in 1824, when the British government bought 36 paintings from a banker called John Julius Angerstein.
In the late 18th Century, there was a trend toward nationalising the royal art collections. This happened in Italy, Germany and France. However, Britain didn't follow this model and instead a series of events led to the establishment of the National Gallery.
First, Angerstein's collection became available. Then it was proposed in Parliament that the government buy the collection, strengthened by a generous offer by Sir George Beaumont to donate 16 paintings. Third, Austria repaid a war debt, which provided the funds to purchase the collection for £57,000.
The National Gallery was originally housed at No. 100, Pall Mall, but eventually moved to its current location in Trafalgar Square. The building was designed by William Wilkins between 1832-8, and the magnificent facade has remained virtually unchanged ever since, despite frequent expansions of the premises in the intervening years.
The National Gallery website is here.