Good Afternoon Jaya,
Travellers can definitely ask at check-in to be moved and subject to availability the check-in staff may be able to do it, all depends on the availability on the day.
The Duty Office does the pre seating but this can be done only 4 days before travelling, earlier than that we do not have access to the seating map. Unfortunately at that point if the flight is busy availability maybe limited.
Also if the Duty Office can fulfil the request BA may change the travelers around at their pleasure and we do not have any control on it.
I hope this helps.
Kind Regards,
Mildred.