As kymmy said, most ADSL even Virgins ADSL will need a BT Line. Even if your new isp does a short contracts your stuck on a 12 month minimum one for your BT phone line, 18 months for their Broadband.
As for ADSL providers, I personally wouldn't go through Tiscali, there are quite a few much better ones.
Try
www.samknows.com and search yoru exchange and see who you can use.
I know Be, Sky and BT all have checkers on their sites to see if you can get their service from your local exchange.
Do bare in mind, that on top of your ISP charge you will also have to pay the BT line rental, even if you don't use the phone.
Most cases BT will charge you £125 new line install fees, unless the hardware has already been installed in the property. Sky i do know if their deal is still on, offer a kind of refund on the BT install fee.
TBH if my new house was able to be cabled up i would not have left a cable network, for all it's faults for most ADSL packages.
It all depnds also on what your going to need the net for, to who or what you change to.