It depends on where you are, I guess.
There is a good coin shop in Cambridge. There is also a good collectibles shop in Birkenhead which has lots of coins. I would recommend both of these. Afaik, both do mail order.
Shows are a good place to get coins and get to know the dealers. Lots of dealers travel round the UK, so might be worth looking at that. Also, have a look at Coin News, most of the active dealers advertise in it.