I'm not sure about the Prospect being London's oldest surviving pub - riverside pub, maybe but for most of it's life it wasn't actually in London. Right by Aldgate bus station is the Hoop & Grapes which is the only timber-framed building in the City to survive the Great Fire.

Here's some other pubs which claim to be the oldest

http://www.google.co.uk/search?hl=en&q=london%27s+oldest+pub&btnG=Google+Search&meta=