Sorry Beany for not reading your original post correctly.
Regardless, I would go online and look up the EU law and regulation on flight cancellation
and read that to the supervisor on the phone. Advise them if they don't then you will be filing against BA in small-claims court in NY as well as taking it up with the UK Civil Aviation Agency. And when they say no, re-state your intentions and escalate to a different supervisor. They are in effect breaking their contract of carriage with you. Threaten them. Get them to make it right. If they don't, then I will suggest going through EU Claim. They can be found at
http://www.euclaim.co.uk/