I think you will be able to swap at the airport (check in or even the gate) without too much hassle, and failing that just ask the crew on board if they could help.
You may have to be willing to accept non-window seats, though.
It does seem a bit silly but these aircraft swaps can leave people all over the place. There will no doubt be others wishing to swap too.

Do you have BA status or did you pay for the seats?