Prince Harry’s return to the U.K. has brought him within miles of his estranged brother, Prince William.

The Duke of Sussex, 40, arrived in his home country on Monday, Sept. 8, for the annual WellChild Awards and other charity visits. Shortly after landing, he traveled to Windsor Castle to privately visit the burial site of his late grandmother Queen Elizabeth and lay a wreath of flowers on her third death anniversary.

Prince Harry arrived in the U.K. in a “positive” mood. “He’s in a really good headspace and looking forward to seeing everyone from his charities and the causes he cares about,” a source tells PEOPLE.

About eight miles away from Windsor Castle, Prince William, 43, marked the Queen’s death anniversary with his wife, Kate Middleton, at the Women’s Institute in Sunningdale, Berkshire, a cause close to the monarch during her life.

Despite their proximity, the brothers are not expected to reunite during Harry’s U.K. visit amid their ongoing rift.

The brothers’ planned engagements throughout the week will keep them farther apart: Prince William will visit a youth organization in the Lambeth district of south London on Tuesday, but Prince Harry will travel about 130 miles north to Nottingham.

Then on Wednesday, Harry will be back in London for an outing at Imperial College London’s Centre for Blast Injury Studies. However, William is scheduled to be in Cardiff, Wales, 150 miles away, to visit a pioneering new mental health hub launching at Principality Stadium.

Prince Harry’s latest return to the U.K. comes after he expressed a desire for “reconciliation” with his family. In May, he told BBC News that he “would love reconciliation with my family. There’s no point in continuing to fight anymore.”

“Life is precious. I don’t know how much longer my father has,” he continued, seeming to reference King Charles’

cancer diagnosis and ongoing treatment.

More positive steps seemed to take place over the summer, with Prince Harry’s aides and one of the King’s key staffers meeting for the first time in July.

“It was a good first step,” an insider told PEOPLE at the time. “It is always better to be talking.”

In another apparent olive branch, Prince Harry reportedly offered to share his official schedule of outings with the royal family. The move not only allows transparency about the Duke of Sussex’s planned events — avoiding conflicts with Harry and Meghan Markle’s public appearances and the royal family’s engagements — but also gives William’s team a clear sense of where Harry will (and won’t) be as they plan out the Prince of Wales’ schedule.

Sharing diaries could also hint toward the two camps finding a time for Prince Harry and King Charles to meet in person. 

The father and son were last together in February 2024, when the Duke of Sussex flew from California to the U.K. to see the King following the announcement of the monarch’s cancer diagnosis. After a brief meeting between the two at Clarence House, Harry left the U.K. a day after his arrival.

There is speculation that Prince Harry could reunite with King Charles, 76, during his current visit to the U.K. amid the recent attempts to ease tensions.

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However, the estrangement between Harry and William is deep, with no communication between them in recent years.

Robert Lacey, author of Battle of Brothers, recently told PEOPLE: “The rift is very profound and very long-lasting. It will not be changed, in my opinion, until Harry makes a move and apologizes.”

Added historian Amanda Foreman: “Everyone wants it to happen on their terms, but that’s what makes it impossible.”