The good news is that all calls made to BT are recorded. The best thing you can do is ring through to COT (the customer options team, you get to them by phoning 0800 800 150 and then pressing the options suggesting you want to cancel) and ask to speak to a manager there, then ask him to listen to the call where you were offered compensation for your time. As long as it's clear the advisor was being specific and referring to actually giving you money and not compensating you in the sense that they'll sort you out a cheaper package or some months free then you shouldn't have a problem.
On BTs residential service it states in the contract that you're not entitled to compensation for loss of service beyond a refund for the days when you paid for the service and it wasn't working, so it's not something that should have been offered to you at all, especially as it sounds like an engineer did turn up on all of the booked appointment dates to do diagnosis work. Despite this, I completely agree that if someone representing BT did make a commitment to you then it should be the company's responsibility to follow through on that commitment.
Also, the person who picks up the phone in COT may be reluctant to take your complaint and try to pass you over to the tech support team to deal with. The correct complaints procedure at BT is that if the person who picks up the phone can't resolve your complaint then they escalate it to their manager, and if she can't resolve it within 4 working hours then she refers it to a dedicated offline complaints team. Make sure to grab the direct dial number for the manager you speak to if she says she'll call you back. BT Managers are all meant to try and resolve issues FPOC (first point of contact, it's a big thing in the company at the minute), so if you get the feeling you're being fobbed off remind them of this.
Hope this Helps!