Thanks for the update - I'd almost given up posting on this site as so few people let you know the outcome of the problem.
I have no experience with Sky - but about 30 years experience as an IT professional dealing with telephone related problems caused by BT - in 99% of cases like this (weird, inexplicable behaviour), what happens is you ring BT, spend hours on the phone trying to find a responsible adult, going round in circles, being told nothing is wrong, and then, (usually about 30 minutes later) the fault miraculously disappears, and BT deny all knowledge of it!