You have to bear in mind that most pubs in central London serve terrible beer. Nevertheless, here are a few centralish suggestions:
The Lamb, 92 Lambs Conduit Street
Princess Louise, 208 High Holborn
Cittie of Yorke, 22 High Holborn
Old Bank of England, 194 Fleet Street
The Lamb and Flag, 33 Rose Street (Covent Garden area)
A couple a bit further out:
Duke of Cambridge, 30 St Peter's Street (this one's in Islington - a short bus or tube ride from the centre - good beer from the Pitfield and Freedom breweries - food expensive and a bit variable)
The Dove, 24-28 Broadway Market (this one's in Hackney, but usually has an excellent selection of Belgian beer, both draught and bottled)
My personal favourite though is The Anchor and Hope, 15 High Hill Ferry, Clapton (E5):
Image:Upper clapton anchor and hope.jpg - Wikimedia Commons
It's easily the best place to sample Fuller's London Pride and ESB, but way, way, way of the beaten track!