I can recommend Graham at Superlative Time in Ealing, London.
http://superlativetime.com/
Copied & pasted from post in General Forum:
Somehow the screw had gotten loose whilst I was washing my Datejust yesturday and some water got in, with condensation appearing on the glass.
Called up Graham at Superlative Time, who urged me to get it to him asap due to possible damage to the parts and dial. Luckily he is on my route to work and I so I arranged to visit him in his workshop the next day.
Right there and then, he removed the movement, and luckily nothing bad seemed to have happened. He invited me to watch as he removed the moisture, checked the case for water resistance and condensation, checked the movement and regulation, adjusted the beat error (it was 2.2ms out), before putting it back together giving me tips on how to adjust the bracelet so it remains tight.
During all this, we had a very nice chat about servicing, showing me the difference between old and new gaskets and the wear that happens to the pivots in a watch movement and why regular servicing is necessary to prevent having to replace parts.
He also asked a very reasonable fee for an hours work and overall I got a really good impression about someone who is personable, meticulous and takes real pride in his work.
He will certainly be getting my custom in the future.