Prince William and Prince Harry [Courtesy]

Prince William today hit back at allegations of racism after Harry and Meghan's bombshell interview, saying: “We’re very much not a racist family”.

The Duke of Cambridge this morning revealed he has still not spoken with his brother since the claims were screened on Sunday.

He and Kate made their first public appearance since the Duke and Duchess of Sussex sensationally made a string of allegations in an interview with Oprah Winfrey was screened on Sunday.

Harry and Meghan alleged an unnamed royal had made remarks about son Archie's skin colour before he was born.

Asked if he had chatted to Harry since the weekend, William said: “No I haven’t spoken to him yet but I will do.”

The comments come as William and Kate ignored their own family problems and promoted a mental health initiative for children on a school visit today.

Faced with competing claims that they and their staff left their sister-in-law Meghan unprotected and suicidal or did nothing to stop her bullying aides, William and Kate signalled their intention to carry on as normal.

They went to School21 in Stratford, east London, to mark children’s return to classes and the rollout to secondary schools of a mental health project for pupils which Kate launched in primary schools in 2018.

On Tuesday Buckingham Palace issued a statement saying that issues raised in the interview, including an allegation of racism, were "concerning", and said the matter would be dealt with privately.

In Sunday night's bombshell interview, Harry and Meghan opened up on their relationship with William and Kate.

Speaking to Oprah Winfrey, Harry hinted at tensions with his brother, saying the relationship was "space".

Prince Harry and Meghan Markle during an interview with Oprah. [Courtesy]

It is understood that William and Kate have decided that there is no need to tailor their programme to avoid subjects uncomfortably close to home.

Children at School21, a state-funded school for pupils aged 4-18, will be given access to lessons on issues such as anxiety and depression from Mentally Healthy Schools.

The lessons are on a website financed from an initial £800,000 grant from the then Royal Foundation of the Duke and Duchess of Cambridge and Prince Harry and launched by Kate at Roe Green Junior School in Kingsbury, north west London, in January 2018.

The future Queen has championed the idea of early intervention by experts to help children struggling with mental health problems.

One in 10 children suffers some kind of mental health issue, often because of problems in the family such as abuse, addiction, neglect, or marital breakdown affecting all social classes.

Course materials have been accessed more than a million times since the project was launched as a pilot in January 2018 and nationally in primary schools in March that year.

It comes as the royals find themselves in the spotlight after Harry and Meghan's scathing remarks.

Meghan claimed that Kate had made her cry in the build-up to her wedding, but reports at the time claimed it was the other way around.

The Duchess of Sussex said that "the narrative" surrounding the incident "was really, really difficult" and "when everything changed".

She later said it was the beginning of a "character assassination", and she claimed she was not protected.

She said: "It was a really hard week of the wedding, and she was upset about something, but she owned it, and she apologised, and she brought me flowers and a note apologising and she did what I would do if I knew that I hurt someone. To just take accountability for it.

"What was hard to get over was being blamed for something that not only I didn’t do but that happened to me and the people that were a part of my wedding going to my comms team, saying, I know this didn’t happen.

"I don't have to tell them what actually happened, but I can at least go on the record saying, ‘She didn't make her cry.

Meghan claims that everyone in "the institution" knew the story wasn't true.

However, she accepts that Kate may have been told not to negate the rumours, saying the duchess is a "good person".

A short statement issued by the palace on Tuesday said: “The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan.

"The issues raised, particularly that of race, are concerning. While some recollections may vary, they are taken very seriously and will be addressed by the family privately.

Prince Harry and Meghan Markle [Courtesy]

“Harry, Meghan and Archie will always be much-loved family members.”