Prince Harry and Meghan Markle’s scathing comments about the royal family have caused a furor across Britain and led to calls for an investigation into racism at Buckingham Palace.

During their televised interview with Oprah Winfrey on Sunday, Ms. Markle talked about having suicidal thoughts and Prince Harry said an unnamed relative expressed concern that the couple’s baby would have dark skin. The royal family has “this mentality of: ‘This is just how it is. This is how it’s meant to be. You can’t change it,’” Prince Harry said. “What was different for me was the race element, because now it wasn’t just about her, but it is about what she represents.”

Kate Green, a senior Labour Member of Parliament, said the comments by the Duke and Duchess of Sussex were shocking and distressing. “I’m sure that the palace will be thinking very carefully about that, and I certainly think people will be wondering what is going to be said,” Ms. Green told Sky TV on Monday. “But there’s never any excuse, in any circumstances, for racism, and I think it is important that action is taken to investigate what are really shocking allegations.”

Vicky Ford, the Minister for Children, told the BBC that while she hadn’t seen the full interview, the allegations of racism were unacceptable. “There is absolutely no place for racism in our society and we all need to work to make sure that doesn’t happen,” Ms. Ford said.

Buckingham Palace has yet to comment on the couple’s television appearance and instead issued a Commonwealth Day message from the Queen, which highlighted “stirring examples of courage, commitment and selfless dedication to duty” during the pandemic.

Last week the palace said it would investigate allegations of bullying of staff by Ms. Markle. At the time the palace said that it “does not and will not tolerate bullying or harassment.” Ms. Markle’s spokesman said the Duchess was saddened by the allegations and that they were the “latest attack on her character.”

The interview with Ms. Winfrey will be shown in the U.K. Monday evening but the fallout has already consumed the British media.

The tabloid press has largely sided with the Royal family, with the Daily Express chastising Ms. Markle for a “self-serving chat with Oprah.” Piers Morgan, co-host of Sky TV’s Good Morning Britain, lambasted Ms. Markle and accused her of effectively labelling the royal family “a bunch of white supremacists.”

During Monday’s broadcast, Mr. Morgan added: “Let’s be clear: Prince Harry and his wife just spent two hours trashing everything the Queen stands for and has worked so hard to maintain, whilst pretending to support her. And they did it while her 99 year-old husband [Prince Philip] is seriously ill in hospital. It’s contemptible.”

But other observers said the interview has dealt a serious blow to the royal family and raised questions about its relevance, particularly for younger people across the Commonwealth.

“We saw a racial clash [in the interview]. We saw a clash across the generations, all much more powerful than I expected,” royal historian Robert Lacey said in an interview. “I think it has posed Buckingham palace with a problem it didn’t expect… The attack on the very roots and functioning of the system won’t go away and raise very important issue.

Mark Borkowski, a London-based public relations consultant, said the interview highlighted just how out of step the royal family was with the modern world. “What [the interview] projected was anachronistic values, racism, bullying, mental health issues; nothing has changed since Diana, and a way of life that actually led a woman to consider suicide,” Mr. Borkowski said in an interview Monday. “That isn’t healthy in a time when businesses, organizations, institutions across the world are rethinking how they operate.”

He expected the royal family will turn to the Duke of Cambridge, Prince Harry’s brother and the second-in-line to the throne, to try to rehabilitate the royal image. But that won’t be easy as long as Prince Harry and Ms. Markle project a more inclusive image. “Not only is the royal brand tarnished but you have a woke, dynamic duo based in California, touched but the royal fairy dust, that has got deals with some of the biggest tech giants in the world. So you’ve got a competing brand,” Mr. Borkowski said referring to contracts the Duke and Duchess have signed with Netflix and other companies.

Many others have come to the defence of the monarchy and insisted that the royal family did all it could to welcome Ms. Markle.

“I certainly recall at the time of the wedding [of the couple in 2018] when I was working as a commentator – and the overwhelming sense of welcome for Meghan and for their marriage,” Charles Anson, the Queen’s former press secretary, told the BBC on Monday. “And I don’t think there’s a strand of racism in that within the royal household at all.”

Mr. Anson added that whatever racism Ms. Markel encountered came from social media and he said the royal household has services to help staff and family members suffering from mental health issues. However, he acknowledged that Ms. Markle’s comments raised “some issues that need to be dealt with within the family context”.