Not sure if this will be of help to you or now, but I recently had a similar situation where I was looking at moving to SKY from Virgin, but was put off by the fact the house had no new BT line so would have had to pay the same £122.50 installation fee. However, after a bit of talking with the local SKY rep he said that Sky would reimburse this cost incurred to get me away from Virgin.
So, if you want to consider Sky as an alternative provider of services, then that might be the answer for you. Just talk to a Sky rep, rather than rely on the website etc.
I actually stayed with Virgin in the end as they offered me an unbeatable deal and I like the V+ box.
Sorry, just re-read your message - surely if your moving house then BT can't hold you to your existing contract? Moving house is normally an exception to T's & C's.