I only recognise two of their picks as places I've drank in, and can definitely agree that both of them belong on the list. They are the "Hand in Hand" in Wimbledon and the "Trip to Jerusalem" in Nottingham.

The latter claims to be England's oldest pub, and certainly looks to have been built in the 12th century as they say it was, so it most likely is. It is next door to Nottingham Castle and would have been there even back in Robin Hood's day. Assuming he was a real person he might well have sampled their ale - in disguise to avoid being nabbed by the next door neighbour, LOL! I doubt if the Sheriff of Nottingham would have frequented a common pub, though.