>>> Could the fault have been fixed remotely before the booked engineers visit?
Yes. I had a similar fault. I found that the problem was actually the incoming 'ring' signal. i.e. if I used my mobile phone to call my landline number, I got the ringing tone on my mobile phone but my landline phone didn't make a sound. However if I picked up the handset, the call was actually there. I tried two other landline phones, with exactly the same problem (thus eliminating the possibility that it was a fault with my phone).
A BT engineer visited my house and confirmed my theory that it was a fault at the exchange (which is only a two minute walk away from my house). So he went down to the exchange to sort things out.
I've no idea about whether or not the exchange fault was affecting other lines as well but let's suppose that it was. If so, when the guy fixed my problem with incoming calls, he'll have also fixed similar problems for other customers too. You could be in a similar situation, where someone else has reported a fault that's turned out to be at the exchange and, in fixing that fault, the engineer has managed to cure yours at the same time.
I suggest calling BT to explain the situation (if you can manage to get past all those annoying "press 1 for this or 2 for that" messages, that is!). If you don't, and BT don't recognise that you had a legitimate problem (even though it's now been fixed), you risk being charged a minimum call-out fee of £150.