Of course, this "Take to and Return to Aircraft Door" service only applies to small strollers/pushchairs. If you pack them into a bag or sleeve, please make absolutely certain there is a handle by which the pushchair can be carried and that the label is clearly readable outside otherwise there is a risk the pushchair may be left behind as "unauthorised."
The BA website asks families to be at the Departure Gate early in bold type for a reason. Please do not leave it until the last minute to rock up - the aircraft hold closes at exactly 10 minutes before Departure Time and any items after this time may be returned to the baggage sort area to be sent as "Rush" on a later flight. It's not to be nasty or awkward that we won't re-open the hold - if the aeroplane misses its departure slot, you may well find yourselves sitting on a remote taxiway somewhere for anything from 20 minutes up to 2 hours waiting for a gap in take-offs to let you go!