Definitely can't be done over the phone. I just called BA and got a rather blunt reply from the agent when I asked if I could split payment for four people across two cards -I'd have to do it as two separate bookings and it's for "security reasons" apparently. I then asked whether I'd be able to allocate seats for those on the separate booking, given we'd all be travelling together and would have booked together.....answer is a flat no -"no sir you'd have to either get them to pay for seating or put it all on the one card." So that means no pre allocation of UD CW seats for e.g.

I wonder if group sales would be able to help here for slightly larger parties? IIRC you can pay them by installments?