I came across this thread while fretting how to claim avios (BA) if I booked on the avis uk site rather than through avisba. The incentive was the avis uk site was £184 cheaper - for a 3 week SUV rental from SEA.

My experience today was that I logged into my preferred account and after being sent round the same loop to choose a car a couple of times I got into the booking process. I got almost to the end of the booking process and had about given up on being able to add BA number when there was a space to enter it after confirming my billing info. Will be pleased if the miles credit but am very happy about the £184 so won't fret too much if they don't.

I thought it was a bit odd that part of the confirmation page invited me to join Avis Preferred even though I was logged in to it at the time. Not letting that burst my bubble.