The Home Office also refused to comment but said such arrangements were decided by the executive committee for the protection of royalty and public figures and were based on an assessment of risk rather than an individual’s willingness to pay for protection.

It is understood the Sussexes flew first class to Heathrow on a commercial flight, accompanied by their own security staff. In the Netherlands, they have been given VVIP status, with the Dutch government affording them enhanced security.

Some royal commentators have suggested that far from feeling exploited by the visit, the Queen, who will turn 96 next Thursday, will have been pleased with the visit from her grandson and his wife.

Ingrid Seward, the editor-in-chief of Majesty magazine, said: “It is a wonderful opportunity to clear the air and offer an olive branch. After everything that has gone on, it must have taken a lot for Harry and Meghan to go to Windsor.

“Also, Maundy Thursday is a very special day for the Queen as it is about forgiveness. She is not one to hold grudges and I think she would have happily welcomed them with open arms.”

A spokesman for the Duke would not discuss details of the visit but said: “We can confirm that they visited the Duke’s grandmother, as we previously said he hoped to do. They stopped by the UK on their way to The Hague to attend the Invictus Games.”