I would ring the UK number during the UK day and evening time if you can, but in principle any BA contact centre can do this. The telephone numbers are in the forum Dashboard. Usually during the check in process there is a stage where you can move seats. So long as you don't print/app/save (etc) your boarding pass you can then revert back into online check in and contine to move seats even though you are checked in. There shouldn't be a problem with this, apart from BA's occasional IT glitches, it's a routine part of the online service and extensively used by others in this forum.