Well the way I see it, if you have the Home Hub / Smart Hub etc connected to your line and turned on, BT would be able to see if there is a fault on your line due to they wouldn't be able to talk to the Hub.
Does your phone line work (assuming its the same line for the broadband) ?
You might of already tried all this, but just in case...
If your phone is working, when everything is connected up, try testing your phone in the test socket, by "CAREFULLY" removing the phone and xDSL Face plates.
If that works, unplug the phone and plug in the hub to that same test socket using a micro filter, does that work?
If your phone is working in the test socket and your broadband still won't work, try any other modem/router you have there and see if any of those work.
So if your phone is working and your broadband still fails to work, then its shouldn't be your wiring.
If you have FTTC maybe the link cable between the PCP and fibre cabinets have come out of broke, or maybe there was a fault some place and an engineer / sub contractor connected your line to somebody else's, have you tried to phone your land line to see if that rings?
If you are on ADSLx your line card in the exchange might be faulty, or by mistake re-allocated to somebody else.
I have as far as I can remember twice had our line here swapped with somebody else's line, BT kept insisting our line was fine until we discovered we had a different number, to which an engineer had to be sent out to resolve the issue.
Basically it could be anything causing this issue.
My guesses are if BT cannot find a fault, then it might be a switched line someplace, so like I said try phoning your landline from a mobile, or use your landline (if working) to phone your mobile, that way you would see if its your line or not.