The two BAE146s that the Royal family travel on, or used to, are Royal Air Force aircraft so if in fact they don't use them anymore, then they've probably been reallocated to other duties.
I really don't know about this one.
About the Queen using Virgin or BMI, well I don't know if the decision is actually up to her.
All I can say is, it was nice to see something really out of the ordinary at my local airport for once where nowadays the largest we get to see are 737-300s and a couple of 737NGs.
Why doesn't one of the world's richest families have their own private jet?
Well, unlike the Royals of Brunei, Saudi Arabia, etc, they would probably come in for a lot of criticism if they did as the British monarchy are largely funded by the British taxpayer and aside from that, it's simply not their style to flaunt their wealth in the same way as the others do.
So, you're not going to see Prince Charles buying Prince William an A340 for his next birthday.
An you're right THOMASKEMPNER, she does in fact use BAs first class cabin.
Do you really expect her to travel Economy?
The reality is that the 777 she used on this trip was a chartered aircraft so it was just her, Prince Phillip and their entourage on board.
Her first ever commercial flight, by the way, was on an Air New Zealand 747-400 from LHR to AKL via LAX and on that occasion, the first class cabin was outfitted just for her.