I am with BT Yahoo. I moved house and follwed the advice given by the BT telephone customer support. They gave me a date and everything of when it was going to happen. Said they would ensure the BB was transferred at the same time as my phone (Moving in same area)- seemed so easy. BUT...
I moved, the connection date came and went but no broadband (this is still within the 12 month contract) I phoned them the next day only to be told I cancelled my broadband????
Anyway after much fighting and listening the opera music while on hold I was told by the BT broadband depatment that I should have contacted them first and they would have ensured the BT phone line would be moved at the same time.
After all the trouble I did get my broadband a week later than expected.
My advice - Make sure they explain every detail to you before hand. Oh yes and they didn't charge me anything (apart from the annoying wait on the phone)
Good luck