I had the same problem with refunding Avios tickets and my only luck was to call +44 0800 727 800 and use options that resembled 'new cash bookings'. All combinations seem to lead to a pre-recorded message or immediate cut-off.

My option combinations are: option 2 for making a new booking and then option 2 again for all other payment methods.

The agent who picked up (after about 10 minutes) transferred me over to another agent (waited for another 5 minutes) who dealt with Avios booking refunds. Avios credited within 24 hours.