stay well away from the many shoe store/watch repair places around town.
Most will turn it away and look there nose up, but there are a few backstreet places, that will help but will say that there is no warranty and if they break something else trying to fix it, its your problem.
There are a few watch places located in the underground stations, but there skill set is limitedt to changing straps, batteries. Some people have used a guy in picadily circus station, but there are as many bad reports as good.
There is a member called Smidsy, not sure which forum who has a good rep.
other options are sending to france or gernany where you have Domi and Wiz.
I needed a tx crystal put in a v6 hub this week, went around town, with no joy then i remembered that the debenams store has a watch repair place on oxford street, they dont do auto movements, but he gave me a look, took my watch and fitted the crystal, came back and said as he cant warrant the work, he wont charge me, result!
There is also a watch repair place near farringdon on top of a sweet shop that do work for the many jewellers in town and work on omega's etc, depending on who you talk to they may or may not help.