Problem solved - sort of, but to my entire satisfaction.
Llondel, you were right. Thanks.
After reading bits on the internet and thinking, I swapped the Line A and Line B wires over on the extension socket in the main box and the call blocker now works perfectly on the extension in my study. As it still doesn't work on the master socket, I can only assume the BT contractor connected up the lines reversed when he installed it.
The good news is that I prefer the base phone on the extension in any case, so I won't bother to even try to take it further with BT; I couldn't stand another morning trying to work my way through their impenetrable maze of phone calls, automated response systems and sub-continent call centres.
Result!!
GG