Signing up to BT was easy. Disconnecting from BE was HARD. Firstly, Sky's call centre is logjammed, no point trying to call them at all. But I guessed that BE's centre is still up and running, and that proved to be the case. I then had to convince two people that (a) I wanted to change, (b) the reasons I wanted to change are that I don't want to do business with Sky and that I can get BT infinity now, and don't want to switch my phone line to Sky. They tried very hard to get me to stay with them, including offering me half price on the next year. But of course you are then stuck with Sky as your ISP and phone provider, and I really don't want to go that route. Eventually I convinced them that I do want to change, and that they must send me a MAC number to make the transition work. But it wasn't easy...
Hopefully this will all go easily at the start of October. If not, and I vanish off line for a few days, that will be why.
Update - got the MAC number and put it into BT's site, they're now able to make the swap a week or so earlier.