Bumping this back up to the top and a call for anyone who can help the OP more specifically please?

I have no specific knowledge or experience on bassinets etc other than it seems like a call up again scenario but it's a possibility your seating hasn't as yet been allocated? Hopefully someone else more in the know will post, fingers crossed.

Here's what BA say.

Selecting seats for an infant on your lap

When you travel with an infant on your lap, you can choose a seat for yourself and everyone in your booking, free of charge, for up to a party of nine. Subject to availability, one person in your booking can choose a carrycot/seat position. If you don’t choose a seat in advance, we’ll select suitable seats for you before the flight.

https://www.britishairways.com/conte...travel/seating

That flight is apparently being operated by a 789 as below and of course there are bassinets seats onboard as per the aerolopa map but not sure what's available and what cabin are they in?

https://www.flightradar24.com/data/aircraft/g-zbkg

https://www.aerolopa.com/ba-789

Pete