Prince Harry and Meghan Markle may have moved back to the U.K., but the rift between the Duke of Sussex and Prince William isn’t any closer to healing.

Sources have told PEOPLE that the brothers remain estranged, with no direct contact between them.

Royal historian Amanda Foreman tells PEOPLE in this week’s cover story, “At the moment, it has gone from being a hot war to a very, very cold war. But in a cold war situation, you still have to turn up to the Olympics.”

Prince Harry, 42, has expressed a desire to reconcile with his brother, but those close to Prince William and Kate Middleton, both 44, say the wounds behind the estrangement remain deep. “It was very hard on them, and I wouldn’t blame William for being cautious,” says one close palace source.

Royal author Simon Vigar says that the Prince and Princess of Wales are approaching the Harry and Meghan situation with the British monarchy’s age-old mantra: “It is keep calm and carry on.”

“They see it as a sideshow and ancient history,” Vigar adds.

While Prince William and Prince Harry remain estranged, there have been steps toward reconciliation between Harry and their father, King Charles. The British monarch, 77, reunited with Harry — as well as Meghan and their two children, Prince Archie, 7, and Princess Lilibet, 5 — in July during the Duke and Duchess of Sussex’s visit to the U.K. before their move. In addition, King Charles and Prince Harry have spoken at least once since the Sussexes’ Aug. 26 arrival back in the U.K. but have not seen each other.

However, that doesn’t change anything for Prince William.

“William’s view is clear — any relationship his father has with Harry or the Sussexes as a family is entirely up to him,” says Russell Myers, author of William and Catherine. “But looking toward the future, he will have no relationship with them, in a working or private capacity whatsoever.”

This fall was already going to reshape life for the Prince and Princess of Wales’ family. Kate, in remission following her cancer treatment, is increasingly back on public duty, while at home she is adjusting to Prince George, 13, no longer being at the breakfast table each morning after starting boarding school at Eton College this month.

Prince Harry and Meghan’s unexpected return to the U.K. has added a complication they didn’t anticipate.

“William and Catherine can maintain that their focus has to be about them and their family, but there will be pressure on them about how they interact with Harry and Meghan and their family in the future,” says Myers.