"Consequently I telephoned BT and was informed that there must be a fault on extension wiring from the main inlet socket".
As a former BT engineer, I can categorically state that this is a default response to anyone with more than one socket. BT are responsible for the line to the NTE, anything beyond that is your problem.
That said, they're not necessarily wrong.
I'll tackle this assuming your internet is ok and your wiring isn't ... (I could be wrong, of course, but I'll stick with what I know).
1.Does the extension wire run across any doorways or under any carpets?
2. How many extension sockets do you have, and what's plugged into them?
3. Is it a 'properly fitted' extension or a B&Q (plug into the main skt and run out the wire) type?