The Director of the British Museum (since 2002) is Neil MacGregor. A previous Director (from 1969 to 1973) was Sir John Wolfenden, who had chaired the Committee that recommended the decriminalisation of homosexuality.
The museum houses a number of items of LGBT interest, notably the Warren Cup.
In 2009 the museum hosted the pre-launch for LGBT History Month 2010, and in 2011 it launched an LGBT Trail. R B Parkinson, one of the Museum's curators, worked on the Trail and has gone on to write a book about the objects, A Little Gay History: Desire and Diversity Across the World.
http://www.britishmuseum.org/explore/themes/same-sex_desire_and_gender/introduction.aspx LGBT page on the British Museum website.