Originally Posted by Reanimation

Okay, so I'll give an update, for future reference about this topic.

The first call to BA was quite rude, "Just wait to be ticketed, could be day before departure." and "There's nothing I can do for you right now".
Second call had more success, managed to get a more proactive agent who with the help of me giving all the flight details and payment details (again) ticketed my flight.

I think for future reference it's good to call BA within 1 week (that is apparently the maximum period that they are allowed to store the relevant credit card details) when not ticketed yet.