I know Browns also have a private space, I've seen them seating people in there for things before. The bar's ok actually, like everywhere down by the river, it can be full of tourists and traders, but because it's at the end of the row of bars, it can be a little quieter.
If it's a weekend you may be able to take over www.thesamuelpepys.co.uk on the north side of Southwark Bridge for your own use - they mention private bookings. No idea about what the food's like but it's not a huge space (so 20-30 would feel comfortable without rattling around) and there's a decent-sized river terrace looking out over Tate Mod and the Globe.
Failing that, the Old Thameside Inn has standard pub grub and might allocate you a section, though it wouldn't be entirely private.