I was woken up early by my main nemsesis, the cold caller.
The call came in at 7:51am (thanks 1471!). I usually wake myself up at around this time. When it's an outside force waking me, it's a different game entirely. I lay there thinking to myelf 'shall I bother?' It rang and rang, so I built up the will and picked myelf up to go into the room to pick it up.
It stopped ringing just as I was reaching for the receiver!
There's no doubt in my mind that it's the new(ish) kind of cold call where they claim to be from BT and inform me that my Internet is about to be taken away. The 'BT' trick seems to have replaced the 'Microsoft' one.
Neither company would call you out of the blue and ask to remotely access your PC. Remember this because there are people out there who were tricked by these people and it cost them a lot of money.