I am in that position myself, and use NTL plus a second line. It's �15 a month for the lot, but there is a company who charge �8 for access only. You'll have to search on 'flat rate internet' but being the cheapest available it should turn up regularly. Unlike NTL they don't give you 2 hours before you have to redial (no idea why), but it's better to get a cheaper 2nd line before choosing the ISP.
The alternative to broadband is a 56k dialup modem over POTS. Perhaps you could get an ISDN line installed which has twice the bandwidth (128k). Best of all, write to BT and see if they can't upgrade the exchange to ADSL (512k - 2M) compatible: I expect you will need a petition of 200 signatures.
There is no alternative other than going back to boring old dial up, using an EXTREMELY expensive satellite modem or waiting for broadband in your area - Sorry!