I use Rose about every 6 months, for parts like olives, brake pads and chain rings, which are much cheaper than in the UK, postage has to be accounted for, so for regular orders, CRC, Wiggle, Ribble, and mainly my LBS are the main places I get parts from. The others which hartsu links to are also good.

A lot depends on the brand, a Euro brand, like B&M lights are significantly cheaper from Germany than the UK, things like shifters, chains, wheels, the UK can be as cheap.

There is a lot of competition for bike parts here, as mentioned Wiggle, CRC, Ribble and PBK who ship the the US, there are also Evans, Planet X (who have a small US operation), Merlin Cycles, Winstanley and many other smaller resellers who drive down prices in the UK.