Received my new (second-hand) BT module from the 'Bay yesterday.
Today I have fitted it. It is blooming awkward to get to! Couldn't actually get the screw undone on the old one. So I have just unplugged it and left it there. I then plugged in the new one and put the glovebox all back in again.
It is now all working fine!
I also bought a little bluetooth receiver and plugged it in to my Aux line in port. Apparently the iPhone (5S) can be connected to both BT devices at the same time. It then plays music through the little receiver (through the stereo) and then switches over to the official BT module to take a call.
Works really well! The little BT receiver was £15 well spent!