First things first. You mention that BT has disconnected your voice line due to you disputing a bill. They would not do this as a "first" measure so there has to be more than this to the story. Yes, your Internet connection will remain for a short time afterwards as this is a different business unit to the voice services, but they will catch on and the service will probably stop shortly afterwards.
Basically no-one is going to offer you service whilst this broo-ha-ha is going on with BT. BT will have tagged the line and whilst you are in contract with them no-one else can put services on the line. Your credit history may also cause some concern, but it may not be a show-stopper.
So it is back to the original issue - what's the dispute? Did you make the calls, or did someone in your family make the calls leading to the size of the bill or is there something else in this equation we don't know about. We try to help here as much as possible, but we do need more information on the basic issue that you have which is not best served by trying to run away from the problems.
SHARK!