Suggest you expect the worst and smile to yourself if your expectations are exceeded.
Not long back from a GB Airways LGW-SSH trip with 1 x 3yr & 1 x 1yr - on arrival at SSH handing agent was waiting at the base of the step with said pushchair - excellent service.
On return flight arrived back into LGW North at 2am (late !) and into one of the gates over the bridge. Lots of crew and 'management' hanging around the airbridge though none of them in the slightest bit helpful - downright rude would have been my opinion when requested by 10+ sets of parents for their buggies. Bear in mind there are no trollies in this area and it's a good 15min walk back to passport control.
Don't know whether this is specific to GB or BA policy but it sucks !!
In summary worth checking directly with your airline before you go and getting a written (email) response from them if positive.