Just got a notification from my bank that the full amount I asked for has been sent by BA. So a turnaround of just under 4 weeks, which is completely acceptable.

This was for replacement flights and transport on Easyjet after a cancellation due to weather.

I still haven't actually received any correspondence from them (not sure where they got my bank details from, unless it was in the claim). I am still 15,000 Avios down, as this flight was due to be in CE and I ended up on Easyjet, so I will see if they'll offer anything additional as a goodwill gesture.