This reads to me as not merely an accusation but that an investigation has taken place, judgement has been cast and punishment dished out. It also appears to exclude any further recourse. On face value this appears to be an egregious abuse of a customer.

I would write to BA, probably by conventional letter with recorded delivery, laying out exact details of the transactions, and insisting the avios get reinstated. Be sure also to set a realistic deadline for BA to respond, I suggest 30 days. Absent any satisfactory response, calculate what the Avios would cost to purchase and commence MCOL action against BA.