Ok, got a call back from a supervisor today, and had an interesting chat. Basically, ticketing won't ticket it as it has to be billed in GBP if I want to pay in the UK, not GIP, and even though it's 1:1, they won't do it - which he apologised for. He was very helpful, and he's going to give GIB a call now, and get the tickets debited from there, and call me back.

Update:

What a performance. The guy from BA in the UK called back saying GIB wouldn't ticket it as it wasn't a GIB based credit card. He was very apologetic about it all.

So I called GIB back myself, and explained the situation. The lady was a little surprised, but checked with the supervisor and said that they did take UK based cards. Oh. Excellent. Here's the number. Five minutes later she called back to say it's ticketed. Got all the ticket numbers, appears in checkmytrip.com correctly. All sorted, tickets to be picked up at the airport on the day of the flight.

Moral of the story:
BA in Gibraltar ^
BA in the UK