I think Her Maj should have her own jet, shared with the Head of Government. Leasing expensive 777's cannot be the way to go. That's what the Queen's Flight was about.
The USofA is putting out a tender to replace the old 747-200's. The tender calls for 4 engines (and I agree with that safety case.)
The RAF have trained 330 (Voyager) crews. Why not procure a second hand (many on the market and so not too expensive) 340-500 (RR Engines) and tart it up with secure comms (for our man with his finger on our button) and a decent interior for Her Maj