Just to complete the story, 1K filled four days before our flight home, the last seat in the F cabin to be filled. When we checked in, the check-in agent voluntarily offered to try and shuffle things around. I explained that I had already discussed it with BA but she insisted on trying because she could see that Pax 2 had previously been confirmed in 1K and then moved without a reason. She was not able to do anything but I thanked her for trying anyway.

On boarding I explained to the lady in 1K that my partner was in 5K and would she mind switching? She agreed without a moment's hesitation, explaining that she really didn't like travelling so far forward.

Some of the responses in this thread have suggested that I've done a bit of a DYKWIA or in some way tried to game the system. At no time did I throw my weight around with any member of BA staff - others on here have noticed my core point that this is about customer service to passengers who have booked in BA's first-class cabin. The moral of the story might well be that a smile and a polite enquiry are sometimes all you need to get what you would like.