"I don't think there is any quick fix," a family friend tells PEOPLE

Prince Harry and Prince William's reunion at Prince Philip's funeral was a first step towards reconciliation.

Although the brothers walked separately in the funeral procession on Saturday, with their cousin Peter Phillips walking between them as they followed Philip's coffin to St. George's Chapel in Windsor Castle, the two were seen chatting naturally as they exited the service.

"I think it's a good start and it was lovely to see but this whole argument runs so deep, I don't think there is any quick fix," a family friend tells PEOPLE in this week's cover story.

Prince William, Duke of Cambridge and Prince Harry, Duke of Sussex
Prince William and Prince Harry at Prince Philip's funeral
| Credit: Gareth Fuller/WPA Pool/Getty Images
5/3/2021 cover Prince Harry and Prince WIlliam
Prince Harry and Prince WIlliam

Insiders say there is a long road ahead.

"Knowing family, it can mend a bit and then can slip back a bit," adds a royal insider.

This funeral marked the first time Prince William, 38, and Prince Harry, 36, had been together in more than a year, since Harry relocated to California with wife Meghan Markle and their son, Archie. 

The Funeral Of Prince Philip, Duke Of Edinburgh Is Held In Windsor
Prince William, Peter Phillips and Prince Harry
| Credit: Samir Hussein - Pool/Wireimage

In the wake of Meghan and Harry's interview with Oprah Winfrey last month, there are ongoing tensions within the family.

During the tell-all interview on CBS, Meghan refuted reports that she made Kate Middleton cry in the lead-up to her 2018 wedding, saying "the reverse happened." (A source told PEOPLE that both women were in tears over the incident.) They also accused the royal family of racism — including "concerns" over their children's skin color — and not getting Meghan help when she felt suicidal.

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William hit back at the racism claims during an outing after the interview aired, saying, "We are very much not a racist family."

When asked if he had spoken to Harry after the Oprah interview, he added, "No, I haven't spoken to him yet, but I will do."

Prince Harry, Meghan Markle and Oprah Winfrey
| Credit: Joe Pugliese/Harpo Productions

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Prince William and Prince Harry not walking together in the funeral procession or into the church was "a practical change rather than sending a signal," a Buckingham Palace spokesman said ahead of the funeral. "This is a funeral and we are not going to be drawn into perceptions of drama. The arrangements have been agreed and represent Her Majesty's wishes."

"The procession choreography, in retrospect, was a mistake," historian Robert Lacey, author of the bestselling biography Battle of Brothers, tells PEOPLE. "As we saw, they could have walked side-by-side quite happily after all. What pleased me afterward was that it all seemed so totally natural, and they drifted to each other like the old days."