Piccadilly Records in Manchester is a fine, fine record store. Originally started back in 1978, it now resides in the Northern Quarter of Manchester and is proudly independant & always well stocked & friendly. For those not lucky enough to be able to get to Manchester, their mail order is good & reliable too.
Probe Records in Liverpool is another legendary store in the North of England. It was born, as was I, in 1971 and continues to stock a great selection of music. It was the emporium of all things weird & wonderful on vinyl for me as a youth & no visit to Liverpool is complete without a visit. If it ever disappeared a part of me would die.
Rough Trade Records is located in London, which is the capitol of England. The stock is great & mail order excellent if you can't there in person.
Boomkat is a great store for both actual & digital releases. If you're the sort for digital releases, you want to give this a place a go ahead of yer iTunes & co. It's better informed & better stocked. You know it.
Bleep is a record store in the ether. It's the store run (is it still, I don't know?) by WARP records. It's great for actual & digital releases, and like Boomkat, is much better priced, stocked & informed than most. Though it's a shame that the WARP shop closed on Division St. in Sheffield way back. I miss that place.
Record Collector is a record store in Sheffield, which despite being the 5th biggest city in the UK (by population) is extremely poorly serviced by record shops.
There are many more stores than this of course. This is just a basic selection, based on personal preference, sentiment & shopping habits. There are plenty of great local places all over the world & I'll happily go in them all given half a chance. I've loved Amoeba in SF/LA, SoundFix in Williamsburg, Avalanche in Edinburgh.