Book it on AA.com, or the UK site in order to pay in sterling, but do it without logging in. When you make the booking you will be able to add your BAEC number via a drop down box just after entering your name, and that will get you the TPs and Avios. More or less the same system with all oneworld airlines, and indeed if you book a BA booking without logging in you could enter an AA number should that be relevant. You could even not bother to do it, and just give your BAEC card over when you check in, not that I would advocate that approach.