Your extension sockets are all wired back to the master BT socket that nobody except a BT engineer should touch - so no, they won't automatically work on your NTL connection if you go to NTL because the NTL installer should put in a completely new master socket and you would have to run new extension sockets off that. That's what we have in our house, but with one wired phone and one cordless in the house, I never found it a problem that the number of active extension sockets in our house dropped from four to two!
There may be something you can legally do to unwire the BT extensions from the BT master and wire them up to the NTL master, but I'm no expert at that so I'll refrain from telling you what I might do and leave it to an expert ...
to Cable Forum, by the way.
