Much depends on which exchange you are connected to - if you go to www.SamKnows.com and look at UK broadband, then do a search and enter your phone number it will come back with details about that exchange.
Since you seem able to get Virgin Media cable, you should have competition from Sky, TalkTalk, and O2/Be Unlimited (but some others may also offer service).
Unfortunately, while Virgin can offer broadband without a phone service (not sure they do, but they have the option to do so), you cannot get any ADSL service without paying line rental for the phone line, however little you use it.
Another option (though only recommended for light users) would be Mobile dongle. I have been using Three and get 15 GB allowance for 7.50 a month, but it was a cut price deal at the start and only when it was due for renewal did it go from 5 GB/month to 15 GB/month. Makes some networks charging 10 pounds for 1 GB/month for iPad/iPhone users seem criminal rip-off !!
However, a few firms undercut BT on line rent by a pound or so, and then the broadband package you want depends a lot on how much data you transfer each month, from simple downloads like updating Windows, to whether anyone in the family 'shares' files via peer-to-peer (while music and films are likely to be illegal copies, other things like linux software may be legit), or if there is use of any TV 'catch up' facility - I have just been downloading some of the BBC shows to play with iPlayer and they can chew up a lot of your allowance.
I am using Plusnet (call centre in Sheffield) and their 'Extra' account (which is probably under 12 pounds, depends where you are) offers 60 GB of data transfer during 'peak' hours (08:00 to midnight) and then they don't count your usage during the night (my downloading in the last 3 weeks has gone just over 100 GB, partly because a bug in iPlayer sometimes makes a programme I have just downloaded 'expire' when I first try to play it, so I end up trying some items more than once).
If you use SamKnows and post/email the exchange code I will be happy to point out which firms are worth considering, if only so you can get 2 or 3 quotes to compare with Virgin Media.
I do get a small (25p) commission if someone tells Plusnet I have recommended it, but would not be using them if I didn't feel they are a reasonable ISP, and I have been using them off and on since 2003 ('off' after moving home, for a while).