Presumably your plumber is qualified, in which case there should be no problem getting an official report on headed paper or with his name and details. I hope it clearly shows the source of the water as being external to your flat. You also need to list the damage to your flat and costs related. You may need to force Southwark to act and then do a claim against them for damages incurred. Keep detailed records of all communications (even attempted comms where they didn't answer phone etc), who you spoke to, time, etc...