Ok, so lets move away from the traditional modes of "public transport". So yes, this is a form of transport, and yes, members of the public will at times use it, but nobody really ever wants to be in the position that it is decided that they "have" to use it.
Yes, it is THE air ambulance. I was under the impression from what I had heard that there was only one (but I might have that wrong) which covered London and out as far as the M25. During the day it is stationed on top of the Royal London Hospital in Whitechapel, but during the evenings it is now stationed at RAF Northolt in South Ruislip and we often see it coming in low over our heads when we are walking the dog in the park in the early evening. It was previously at Denham Airfield in Bucks, but is now closer to town for operational and cost advantages http://www.londonsairambulance.co.uk/news/642-news-move-to-raf-northolt