"When Sloane retired in 1741, his library and cabinet of curiosities . . . had grown to be of unique value. He had acquired the extensive natural history collections of William Courten, Cardinal Filippo Antonio Gualterio, James Petiver, Nehemiah Grew, Leonard Plukenet, the Duchess of Beaufort, the rev. Adam Buddle, Paul Hermann, Franz Kiggelaer and Herman Boerhaave. On his death on 11 January 1753 he bequeathed his books, manuscripts, prints, drawings, flora, fauna, medals, coins, seals, cameos and other curiosities to the nation, on condition that parliament should pay to his executors £20,000, which was a good deal less than the value of the collection. The bequest was accepted on those terms by an act passed the same year, and the collection, together with George II's royal library, etc., was opened to the public at Bloomsbury as the British Museum in 1759. A significant proportion of this collection was later to become the foundation for the Natural History Museum" (Wikipedia article on Sir Hans Sloane).
Roughly six month's after Sloane's death, on June 7, 1753, King George II gave his Royal Assent to the Act of Parliament which established the British Museum. The British Museum Act 1753 also added two other libraries to the Sloane collection: the Cottonian Library, assembled by Sir Robert Cotton, and the Harleian Library, collected by the Earls of Oxford. The long title of the act was "An Act for the purchase of the Museum or Collection of Sir Hans Sloane and of the Harleian Collection of Manuscripts and for providing one general repository for the better reception and more convenient use of the said collections and of the Cottonian Library and of the additions thereto." In 1757 the three founding collections were joined by the "Old Royal Library" assembled by various British monarchs. With these four foundation collections the British Museum became both a national museum and a national library.