The Woolpack on Bermondsey street has an outside terrace. I hate the pub as it's usually full of the after-work crowd, who are generally unpleasant, but if it were at a weekend, you may be able to reserve the patio area out the back, and it's much nicer at weekends.
Rose & Crown in Colombo Street (off Blackfriars Road). They have a really nice garden which is part of the park around the church. Again, don't normally open on weekends, but might for a private hire. Worth a try anyway.