The Angel, 101 Bermondsey Wall E, London SE16 4NB. Equidistant from Bermondsey tube station and Rotherhithe Overground station. Nearby Mayflower is reasonable too. The Angel is a Sam Smiths pub and a very niceley maintained 18/19th Century building
Is that the one that's over the road from a ruined palace (occupied by one of the early Edwards IIRC)? If so, I was going to suggest that (although the OP wants west, so for next time maybe.)
Founders Arms, Right on the river by Tate Modern
The last time I was there I was amazed by how (relatively, this is London after all) cheap the drinks were - given the tourist central location I'd expected them to really jack the prices up.