I must add though that I didn't ask for an engineer visit, the guy on the end of the phone did a test, and said that there was a fault and that he was going to send one. Does that mean I could still get charged - even though they say there is a fault?
It depends on what fault they think they saw, what type of visit they have booked the engineer for.
I'd say don't cancel.
At very least you'll be able to see a PQ test done on your line .... earwig over the engineers shoulder, ask them to explain each of the results as they come in (if they don't know, well then, I'm sorry) Pay especial heed to a nice balanced pair of results (no more than 5 nanofarad's difference) between the A and B legs, and a good high A/C balance, preferably over 60db, this being your pairs ability to repel external signals (amongst other things).
They should put the tester in manual sync mode (the scripted one they are obliged to run ain't worth a [censored]) look at the errors screen, hopefully they will be piling in, and they'll have something to chase.
I wouldn't worry about a charge, if raised, you could always argue that the CP raised the task.