Booking a bassinet with British Airways

I'm flying back to the UK on Sunday with my 10 mth old baby and wanted to confirm we had the bassinet.  In the past, my travel agent has always managed to secure this prior to our trip. However, I just got this message from him:

BA now have a system where passengers reserve the bassinet upon check-in / on board (we are no longer to able to request these via our reservations system). 

Now I'm wondering whether to use the in-town check in, 24 hours in advance to try and ensure I secure the bassinet?  I also think that the smaller babies have priority in bassinet allocation.  I'll keep you posted as to what I decide to do!  Don't fancy having my lump of a 10 month old sleeping on me the entire journey....