BlankBox, yes, thanks, we knew what the allowances are. And we had weighed the bags on the bathroom scales, both under the 23Kg even allowing for error with the scales. The tip we learned is to put the heaviest through the auto bag drop first, so that if it's overweight you can cancel the transaction and transfer stuff to a lighter bag. (Once you've labelled it and confirmed that, the bag disappears.)
My real gripe is the excess charge of £65 for 1.5 Kgs. I have been on the other side of the counter in the past, handling BA inter alia, when people turned up with hugely excessive hold baggage, and happily charged them for it, sometimes on BA's behalf. But I could never in all conscience have asked for £65.00 per 1.5Kg on any flight, let alone the short-haul one we were on the other day. It is simple extortion, and BA should be thoroughly ashamed.