I'm fairly certain that the £125 is if they need to physically to put a line into your house. When I got my BB with Sky I didn't have a phone at all but did have a line in. The engineer from BT came along and just connected it up, tested the line and they allocated a number.
With you having a phone already I think you may not have to pay the big installation fee. You'll probably find that the existing line is BT's anyway.
Maybe someone with a bit more actual knowledge of telecoms could confirm or advise to the contrary...
JJ
You gotta tie yourself to the mast my friend, and the storm will end.