You may want to go on a pub crawl offerred by the London Walks. I went last year and had a great time. I did the Hempstead Pub crawl and we went to three pubs ( including the Holly Bush which is really nice) and did a walk around the area. The guide was great, the area was like a charming village and you did not feel like you were in London, and they leave you right near a tube station.
This way you get to see pubs you would not normally go to. I am going to do that again this year while in London. At least one if not two. They start around 7 or 7:15PM, they have a web site which will explain it all.
I also liked the Counting House.