BT advertises that a visit of an Engineer will be charged, but I am yet to hear of anyone whose has been charged.
A few years back I had occasion to contact BT, because the broadband speed was very low. My line was tested from the call centre in India and was deemed to be alright. However, I would Not accept the position and was offered a visit by an engineer and accepted on the basis that I would Not be charged. A test of my line back to the exchange revealed a fault which was not showing-up from the exchange end. The engineer told me that it was not unusual and he said that all he could do was to book the fault for attention by Exchange staff. A few days latter all was back to normal.
Might be worth telling BT that you would like the line to be tested from your home as well has any test from the actual telephone exchange. Also try testing your broadband speeds with BT's official on-line tester. :-
http://diagnostics.bt.com/login/?workflow=Speed
Hans.