In reply to Castleman:
THe tate gallery some times does all night openings. THe natural history and science museums do special overnight events, but I think they are meant for school age children.
I would also be tempted to phone london tourist infomation as they might know of things that are specially going on on the date you'll be there.
You could always go to billingsgate market www.cityoflondon.gov.uk/Corporation/our_services/markets/billingsgate/