The fee to cancel or change a BA Avios ticket is $55 online or $80 over the phone. However online you can cancel an award for just the lower of $55 or the taxes paid. For a domestic ticket that means a cancellation fee of just $5.60 (nonstop one-way), $11.20 (connecting one-way or nonstop round-trip), or $10 (connecting round-trip). That’s another reason I like one-ways, I can cancel and rebook the return flight for just $5.60 and I won’t lose my outbound flight. That’s a $50 savings. Flight cancellations must be done more than 24 hours before the time of departure or else you will not get your Avios back.
After cancelling a flight just logout of your BA account, and then log back in and the points should be back in your account.
Note that you have to call to cancel a flight within 24 hours of when you booked it. There is no fee for award cancellations done over the phone if they were booked within the past 24 hours.
When cancelling on line be sure to click through to the last page 'confirm cancellation' and then get 'Your booking has been cancelled'.
Officially you can't cancel within T-24 but I was able to on my third HUCA.
Within T-4 they are a lot stricter.