Prince Harry and Meghan Markle have apparently refused an olive branch invitation from his father, Prince Charles, after arriving in Britain for a short trip.

The Duke and Duchess of Sussex are reported to be staying at their home on the Windsor Castle estate, Frogmore Cottage, ahead of engagements in Britain this week.

It follows Meghan’s revealing podcast and a bombshell interview with American magazine The Cut last week, in which she opened up about “losing” her father and how it “doesn’t have to be the same” for her husband and the future king.

Meghan spoke about her estranged father Thomas Markle and reflected on the relationship between Harry and the Prince of Wales during an interview at her California home.

Harry’s relationship with his father has been said to be tense since the couple’s departure from being working royals.

He said during their televised interview with Oprah Winfrey last year that Charles had stopped taking his calls.

However, it emerged on Monday that Charles had invited the couple – who are in Britain without their children, Archie and Lilibet – to stay at his home on the Balmoral estate. While there, they would have been able to see the Queen, who is also at Balmoral.

“Prince Charles did indeed invite them to stay with him up at Balmoral with the Queen, but so far they have refused,” The Mirror royal editor Russell Myers told Nine’s Today Show.

“So they will be skipping a meeting with the Queen, which is quite sad to be honest.”

Miles said tensions between the extended royal family and the Sussexes remained, with Harry’s memoir due out within months and Meghan’s recent revelation she kept a diary while she was a working royal.

“There is a lot of nervousness around these two at the moment,” Myers said.

“There was dumping after dumping on the royal family and people are very, very aggrieved by it.”

Harry and Meghan have engagements in London and Manchester early this week. They then fly to Dusseldorf in Germany for an Invictus Games promotion, before returning home to California.

Among other family members they will reportedly not see during their short British visit are Harry’s brother Prince William and his wife Kate Middleton.

The Duke and Duchess of Cambridge and their three children have recently moved to a house on the Windsor estate, and will the two brothers will be only about a kilometre apart while Harry and Meghan are also there.

However, royal expert Christopher Andersen told Us Weekly that not only were there no plans to catch up, the Cambridges were “trying to avoid” the Sussexes.

“It’s going to be interesting in the next few days when Harry and Meghan go to Europe, and they’re going to be playing royal hide and seek,” he said.

The Cambridges were at Balmoral at the weekend. They will head back to Windsor this week ahead of Princes George and Louis and Princess Charlotte starting a new school on Thursday.

“They’re going to be, literally, a brief stroll [away from] each other on the grounds of Windsor because the Cambridges have to [return in time to get their] kids in school,” Andersen said.

“It’s going to have all the markings of an old-fashioned farce with these people trying to avoid each other … They don’t want to see each other because everybody’s worried about the [Harry’s memoir]. Harry’s book is going to be loaded with, obviously, bombshells.”

Last week, a royal source said Prince Charles would be saddened if Harry felt their relationship was lost, adding: “The Prince of Wales loves both his sons.”

-with AAP