There is a wonderful old fashioned pub on Lant Street just round
from borough tube station. Small and free juke box.
It's called the gladstone arms.
Can be a bit quiet at times but the locals are friendly.
.. or if you're feeling really brave there's The Fort on Grange Road! Other than that there's the Jubilee Tavern in Waterloo or the Vauxhall of course. In Southwardk there's Warriors and XXL. Kennington has two - can't remember their names at the moment.
The Gladstone in Lant Street is the only one I can vouch for. Good crowd and friendly. I must admit, given the size of the gay community around this way, i'd have thought there'd be more pubs. Apparently not.
I think these messages have summarised pretty well, though the White Swan in Limehouse is reasonably accessable via the DLR from Tower Hill. Like the idea of a new venue in the Tower Bridge area, but pro tem a glass and a bite by the river would be nice!