I don't know of a comparison between US and UK. I do know that if you've been messed around and the shop won't make good on it, Trading Standards have a fine selection of very effective LARTs, and if you bought something mail-order the distance selling laws kick in as well, which are remarkably consumer-favouring. The consumer can, with sufficient persistence, apply the fine British bloodsport of bureaucracy to a satisfactory conclusion.

Extended warranties sold by the shop are pretty much useless - if the offered warranty is a year and it breaks in 366 days, you will have an at least arguable legal case that the device was not quite fit for purpose (YMMV, be prepared to put it quite a bit of effort). Extended warranties sold by the manufacturer if they do repairs in the country may not be useless. Be very sceptical of such offers in general.