There are a growing number of great independents in the UK.
I would recommend frequenting some of the Coffee Forums in the UK, such as Coffee Forums UK, TooMuchCoffee, CoffeeGeek and CoffeeTime to get a feel and check out the cafe reviews sections.
In London there are at least 10 cafes that I could recommend
Life in the provinces is a different story, with maybe 1 and sometimes 2 decent independants operating in a smaller city.
There are some good baristas working at the chain stores as well and it is a case of finding one who goes outside of the standard issue procedure (every now and then ;) to hand craft a nice coffee.
Where did you intend moving to?