Going to London

Here are a few of my suggestions (some of which have already been mentioned):

Farringdon/Clerkenwell:
Craft Beer Company (Leather Lane, superb beer selection)
Olde Mitre (Ely Place, closed weekends)
Jerusalem Tavern (Brittan Street, closed weekends)
Dovetail (Jerusalem Passage, if you have a craving for some Belgian beer)

Covent Garden/Soho area:
Harp (Chandos Place, wonderful pub, one of my personal favourites)
Dog and Duck (Bateman Street)
Old Coffee House (Beak Street)
Ship and Shovell (Craven Passage)

London Bridge/Borough:
Market Porter (Stoney Street)
Wheatsheaf (Southwark Street, I think)
Rake (in Borough Market area, can't remember the street name)
Royal Oak (Tabard Street)

Old Street area:
Wenlock Arms (I think it's still open, but maybe not for much longer?)
Old Fountain (closed at weekends)

Misc:
Euston Tap (just outside Euston railway station)
Southampton Arms (Highgate Road, great cask beer range, one of my favourites)
White Horse (Parsons Green, great beer selection)

Also, don't forget that many other exellent drinking destinations are only a relatively short trip out of London by train.