I don't believe the flights you mention ever existed. They were going to start, I don't think they ever did.

I don't think "air taxi" and "reasonable price" are two things that go together. Air taxis are cost-effective if there is a group of you travelling, but not for just one or two.

Train isn't as bad as the previous posters said - it's around 2.5 hours city centre to city centre, probably not much slower than driving and leaving your car at a park-and-ride. You need to get from Kings Cross to Paddington which is relatively painless.

PS Just read the bits you added to your post. What's your definition of a "proper connection"?