The basic choices are ADSL over a BT phone line or cable broadband over a Virgin cable. For ADSL you need to get a phone line installed, for cable you need to get a cable installed.
Given those are a no go you could try Urban Wimax (a wireless broadband provider) or one of those wireless phone dongles. Of these I'd look into Urban Wimax first.
I doubt that the wireless options provide "unlimited" at a price you are prepared to pay.
http://www.samknows.com/broadband/exchange/WRECT