Apologies if everyone travelling with an infant who does not have its own seat already knows this, but while browsing the BA website regarding carriage of push chairs, I found out that such an infant entitles you to reserve specific seats for everyone in your party, up to nine passengers, free of charge and as soon as you book.
Our new grandson will be coming with us in the summer, so I have secured 8 good seats. Normally I am too stingy to pay £25 a head each way to reserve in advance and have to sit finger poised ready to click on the BA site 24 hours before our flight when free reservation becomes available. Hope someone finds this info useful.