I flew a Beechcraft King air into Heathrow in the early 1980's and it was not a big deal. In the 1990's a BA manager owned an ex Hamble Piper Cherokee and he arranged to fly it into LHR at about 1 am and parked it in the BA hangars where the engineers spent a couple of days preparing and respraying it and then he flew it out again also in the early hours. He had a beautiful paint scheme and it was all done very cheaply. I very much doubt it would be possible these days. Having said that a few years ago I was taxing out at Heathrow, departures were halted briefly as 4 helicopters took off simultaneously from the terminal areas. I think it was a wedding party for someone extremely wealthy. (He certainly would not have been quite so wealthy after that.)
Reference a previous post I too have flown into Dallas Fort Worth in a Cessna 172 and a Cessna Cardinal, almost 40 years ago. Everyone was up in arms because it used to be free but they had just introduced a $7.50 landing fee! On one occasion they told me to land on a taxiway so I did. It was quite exciting taxiing out behind a queue of DC10's. ATC were very good and used to say to the guy in front, "Go easy on the power 'cos yah got a li'l fella behind you. "