I work with a couple of friends who are tattoo'd up all over. I have asked them for recommendations for the sleeve I want doing and they both recommend Nine tattoo in Brighton.
Best to pop into a few though and have a look around.
I spent a whole day with Neil at tattoo fx the other day and he is very good (6 month wait though). Was very hard work and still two more days to do. Have been tattooed by Chris Higgins too. Would recommend both
I'd recommend Robin at 'Bat Country' on Blatchington Road in Hove. Very talented young man indeed. Everything he does is bespoke. He's normally a 4-5 month wait.