It pays to be an Executive Club member in these situations.
From BAs website:-
"Reserve your seat for free during check-in
Once check-in opens, from 24 hours before departure, everybody can choose their seat for free, although your choice may be limited.
Choose your seat in advance for more choice
Whether you want extra legroom or to sit together as a group, you can reserve your seat in advance. It's easy to do, either at the time of booking your flight or afterwards by using Manage My Booking. When you make your seat choice online, we will tell you whether you have to pay or not.
You can pay for seating if you are travelling on any flight operated by British Airways, BA CityFlyer, our franchise partner airlines or a British Airways flight operated by American Airlines.
Some people can reserve their seats for free
Executive Club membership cards.
Executive Club Members plus companions
Choose your seats free of charge for everyone in the same booking if you
are a:
•Blue Member - from 24 hours before departure, when check-in opens
•Bronze Member - from 7 days before travel, except exit row seats and on British Airways flights only
•Silver Member - from time of booking, except exit row seats
•Gold Member - from the time of booking
If you decide not to reserve your seats in advance, we'll do it for you 5 days before departure. If you can't be seated together, we'll make sure each child is seated with an adult from your group"
In your case I would get the reference from the agent and see if you can choose the seats now. You will likely have to pay for reserving each seat unless you are an Executive Club Member.