The Sussexes were spotted in Windsor by a coachload of tourists who were there for the Maundy Thursday service.
One told The Sun: “I couldn’t believe it when I saw who it was. We waved and they waved back.
“They looked happy and relaxed and waved to everyone on the bus. Charles and the Queen were at Windsor Castle at the same time so they must have met them both.
“It was quite the sight. We knew we might see Charles and the Duchess of Cornwall at the ceremony but never believed we would bump into Harry and Meghan.”
The Duke of Sussex is currently embroiled in a High Court legal wrangle with the Home Office over his security status.
It follows an incident in London last summer, when his security was compromised after his car was chased by paparazzi photographers as he left a charity event.
He is seeking judicial review of the Government’s decision not to provide police protection for him and his family when they are in the UK.
He is also suing the Mail on Sunday over what he claims was a defamatory article on the subject, which is said to have caused him “substantial hurt, embarrassment and distress”.
The Duke faced criticism for failing to return to the UK last month for a service of thanksgiving for his grandfather, the Duke of Edinburgh.
The Duke appears to have no similar security concerns when it comes to travelling to the Netherlands for the Invictus Games. About 300 journalists are accredited for the event and scores of paparazzi will be there.
The couple will be protected around the clock by their private security team, as well as the local authorities.
The Dutch national police’s DKDB Royal and Diplomatic Security Service is said to have overall security responsibility.
It is not known where the couple will stay but Soho House Amsterdam, where they have stayed before, is a possibility.
They are good friends with Markus Anderson, the private members’ club executive, who sat next to the Duchess at the opening ceremony of the Invictus Games in Toronto in 2017.
Founded by the Duke in 2014, the Invictus Games has twice been delayed by the coronavirus crisis.
The event, inspired by the Warrior Games in the United States, aims to help wounded and sick servicemen in managing their recovery.