You can join them to the BAEC (only as a HHA member) since if they occupy a seat then they (well, you ) will have paid the appropriate child fare, which IIRC is eligible for miles and TPs. Of course, if you have to move countries, you have to dissolve the HHA and reform it (by far the easiest way) and the dissolution closes the infant's account by default. On the plus side, the head of the HHA gets their miles (not the TPs though )

Happy flying Shuttle-Bored, and thanks to the others for the responses. Will book a third seat I think, since the idea of an 8 hour flight with a squirming infant with no seat is not a good one - and we're planning on travelling just before Christmas...