I guess the problem now is that the OP is three days on from the flight arriving. Had the replacement been bought immediately, there would be no question that BA would have paid out. Now the pushchair may well be on the brink of being delivered given it's made it to the UK, I sense - not with any degree of certainty, more a hunch - that BA may be somewhat less keen to play ball. "You managed without it for three days Sir/Madam, are you sure it was reasonable to now need one for less than a day?"

This would certainly be a case where I'd personally not want to spend more than I was prepared to lose.