BA.com will typically charge you in the local currency or whatever currency BA denominates for that origin. As you note when that gets charged to your card it will be in the foreign currency and Amex will apply their exchange rates and charges to convert it to £.

If you want to be charged in £ so that the charge to your card is not in a foreign currency you would have to call to book it. I have found when making bookings on the phone with BA they will default to quoting and charging me in £. Unfortunately I think you would be charged the offline booking fee if you call to book.