Try www.SamKnows.com and use their Exchange Search link down the left side.
Enter suitable info (phone number or town name) and it should come up with the local BT exchange you are on.
From that, you can see a list of alternative suppliers (in the lower right hand side, marked LLU - there may be from 1 to nearly a dozen, rural areas unfortunately sometimes have no alternative firms). One disadvantage of using an LLU firm, however, is that it might be more awkward to switch to another ISP some time in the future if you decide to change again, so do also look at ThinkBroadband (link below)
As CAUP says, BE (unlimited/O2) has quite a good reputation, as does Zen, but cost wise there are many other options.
Look at www.ThinkBroadband.com and there's an ISP search facility, so you could look for ISPs which don't lock you into long term contracts (some are now tying new customers for 12, 18 or even 24 months).
You can also do a comparison of up to 6 ISPs, and will be shown graphs of the speed, reliability and customer service rankings for them for the previous 6 months or so, just so you can see whether existing customers are generally happy - it sometimes shows quite large differences between ISPs, and expensive does not always guarantee a better/ faster/ more reliable service.