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It depends what the watch is. Very little watch servicing seems to be done in London now (to the extent that you can walk in somewhere, drop a watch off, the guy out the back does it and you can pick it up a few days/weeks later). Alsal is that, and they're fine, but I wouldn't take something fancy/valuable there (they probably wouldn't even accept it).
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I haven't used them but I know some jewellers send stuff to these guys in Hatton Garden
https://perriwatchrepairs.com/
I have used https://watchguy.co.uk/ a couple of times, very happy, think someone else here used them too after I mentioned them before. You have to send the watch off though...
Forum approved place for servicing in London?