Some women can get through the "visual appearance" filter at the check-in by the way they dress; we boarded a lady in full Arabian Gulf rig, on the heavy side perhaps, but then many women are.
10 minutes later, on route from Dubai to Abu Dhabi in a BAC 1-11 galley, she gave birth to a healthy, full-term baby. It was not her first by any means and she needed no help. She simply wanted to have it born in Abu Dhabi, for financial reasons, and the baby was a day ahead of its STA. This was before a road existed all the way; the taxi ride took about 4 hours on sabkha tracks and was a jolting experience.
(Gulf News headline next day; "GULF AVIATION, AN EARLY ARRIVAL AT LAST".)
I know your interest is in births on flights with a UK destination, but that tale shows one reason there are airborne births.