When I was looking into this I found that most 95% of the ADSL options require a BT phone line. So, you pay at least £10+/month in addition to the ADSL rental cost.
The exception I looked at was TalkTalk where you pay them for line rental instead, being from New Zealand it wasn't a bad option as I could pay £20+/month and get free calls to NZ anytime day or night.
There are other things to consider with a switch like this:
1. Once you have been 'unbundled' from BT to TalkTalk, which involves physically moving your phone line in the telephone exchange, you may have to pay BT to be moved back if you later decide to do that.
2. I'm not sure what speeds you're likely to get with TalkTalk, part of unbundling is moving from BT hardware to TalkTalk hardware which may be better or may be worse. I know one person on TalkTalk and they had a period with absolutely rubbish speeds which lasted for a week.
The main problem with TalkTalk is the minimum 18 month contract. You can break early but will still have to pay the remainder of your contract, or their costs, whichever is less.
I looked at cable too and found that Virgin Cable was a good option. You can get basic/slow unlimited* cable for £10/month and you do not need a BT line. Unfortunately you can only have 1 cable connection per household so due to my flatmate already having cable I couldn't get my own. They have a 12 month minimum contract period.
* subject to fair usage policy.
Of the various ADSL connections out there I was impressed with the PlusNET website, they don't offer an unlimited service, instead they offer "FREE Overnight Usage", the reason for this is that most unlimited connections have a 'fair usage policy' which realistically restricts your connection, therefore it's not 'unlimited' and to market it as such is dishonest. I have no idea what their service is actually like but they do describe their connection options in terms of gaming and prioritising for gaming, who knows.
In the end I made a deal with my flatmate to share his cable, I pay 1/2 the monthly rental and it's working out great. The wireless router I installed is working perfectly
I started my search
here, it seems to list most providers.