Hi, the fact that the noise is a great deal more audible to you than the caller would generally indicate the fault is located close to your end of the circuit.
Your following statement really sets the alarm bells ringing, if you will forgive the pun.
One thing I think I need to resolve is that we have concealed joint behind the plaster where the line comes into the house, one sort of cable goes in from the outside, and a different type of cable pops out of the plaster and runs to the socket.
If your issues are BB related remember it is delivered via the copper pair so this really needs to be addressed believe me, as no engineer IMHO worth his salt would be prepared to rely on a measurement taken from the the internal wiring, if as you state it is purely a PSTN issue it still needs to be addressed, as most noisy lines will " LINE TEST OK" so a non service affecting hard fault(Battery/Earth/Loop/Capacitance/AC balance) condition may have been cleared, yet you still have a High Resistance Fault (noisy line).
Please,please,please find and expose that plastered over joint (it will always be problem) and make everyones life that little bit simpler.