I'm fairly sure that the Duke and Duchess of Cambridge were conveyed in RNZAF and RAAF aircraft when they visited Down Under earlier this year for part of the journey there and back. I believe for the near-UK legs the usual charter arrangements were in place.
While I agree that the fleets of modern biz jets operated by some near-bankrupt states is positively obscene, I do think that our own Head of State and high ranking government people should be conveyed around by modern, appropriately equipped aircraft operated, maintained and crewed by the armed forces.
Talking of modern, No.32 Squadron's fixed wing aircraft are all in the region of 28-30 years old now.