Not so much "met" as "nearly ran into". David Cameron, then the UK Prime Minister. He was out jogging in London with a police protection office and I nearly ran into him. I only figured who he was after he had gone.
I met the members of a few Christian heavy metal bands back in the late 80s/early 90s. Seventh Angel, Detritus, Whitecross, One Bad Pig etc. Not famous unless you're into that genre.
Probably the most famous person I met and talked with would be Chris Packham. He's a British naturalist and was involved with a nature-related charity at the same time I was also involved. He was a really nice guy.