Adnam's have their only London pub on the south side of the bridge: The Bridge House[/url:15vxdsm0], though the reviews aren't great.
The Kernel Brewery[/url:15vxdsm0] is nearby (south of the river again) and it looks like a few of the pubs around Bermondsey carry their beers.
Most importantly, you're only a hop-skip-and-jump from Borough Market: the foodie and beery centre of London. Great selection of cask ales at The Market Porter[/url:15vxdsm0], a (pricey) brewpub down the street in BrewWharf[/url:15vxdsm0], and round the corner there's The Rake[/url:15vxdsm0] for some serious world-beer geeking. The Rake people also run the Utobeer off licence stand in Borough market itself which has an amazing selection of bottles -- handy if you're not flying hand-luggage-only.
On the edge of Borough at London Bridge, is Fuller's Barrow Boy and Banker -- I'm told it's one of the few pubs that carries London Porter on cask all year round, so is well worth nipping in to.