The Government will be “guided” by the royal family on any decision to formally strip Prince Andrew of his titles, as the Prince of Wales reportedly intends to take a more ruthless approach to his disgraced uncle and ban him from his future coronation.

Heir-to-the-throne William was consulted on the decision that led to Andrew relinquishing his dukedom on Friday, but The Sunday Times said William “knows the ‘Andrew problem’ will be in his in-tray at some point”.

The newspaper claimed future king William will be “more ruthless” and is “not satisfied with the outcome”.

Meanwhile, it has been reported that Andrew tried to get the Metropolitan Police to dig up dirt for a smear campaign against his sexual-assault accuser Virginia Giuffre.

The force said it was looking into the allegations after the Mail On Sunday claimed Andrew passed Ms Giuffre’s date of birth and social security number to his taxpayer-funded bodyguard in 2011 and asked him to investigate.

Energy Secretary Ed Miliband told Sky News’ Sunday Morning With Trevor Phillips that the issue of Prince Andrew’s titles was one for the royal family to decide.

He said: “I think in this we’re going to be guided by the palace and the royal family.

“Obviously, all of our sympathies and the sympathies of your viewers at this time are with Virginia Giuffre and her family as to these really concerning set of issues.

“But I think it’s really important as a Government minister, that we allow the royal family to make decisions on these questions.”

He also described the claims that Andrew wanted his bodyguard to smear Ms Giuffre as “deeply concerning allegations”.

He told the BBC’s Sunday With Laura Kuenssberg: “These are deeply concerning allegations. I think people want to look at those allegations and what the substance is behind them.

“But if that is correct, that is absolutely not the way that close protection officers should be used.”

Andrew, still a prince and living in the 30-bedroom Royal Lodge mansion, issued a statement in his own words on Friday in which he said he was giving up his Duke of York title and honours to prevent distracting from the work of the monarch and the royal family.

Ms Giuffre’s brother Sky Roberts has urged the King to go further and strip Andrew of his right to be a prince.

William is always understood to have wanted to take decisive action with regard to the long-running controversy surrounding Andrew and his links to paedophile Jeffrey Epstein.

The newspaper reported that when William is king, he will ban Andrew from all elements of royal life – public and private – including his coronation, and most state occasions.

It added that William will also ban Andrew’s ex-wife, Sarah Ferguson, from royal events, but their daughters, his cousins Princess Beatrice and Princess Eugenie, will still be welcome at family and official gatherings.

Kensington Palace declined to comment.

Andrew’s standing with his relatives was laid bare during the funeral of the Duchess of Kent in September, when he tried to engage William in conversation.

William did not respond to comments made by his uncle, who stood by his side on the steps of Westminster Cathedral, staring straight ahead and barely acknowledging Andrew’s presence.

The King has already ruled that Andrew will no longer attend the Christmas Day service with the royal family – and the statement on Friday was viewed as a final banishment for the prince after the ongoing drip-feed of scandal over the years.

Charles previously allowed his younger brother to attend his 2023 coronation, with Andrew arriving decked out in his Order of the Garter robes.

A year earlier, the then-Duke of York paid millions to accuser Ms Giuffre to settle a civil sexual assault case, despite claiming never to have met her.

Andrew has also given up his Garter knighthood, meaning he will no longer be able to wear his robes or attend the Order’s annual service at Windsor Castle each June.

There had long been calls for Andrew to lose his dukedom, given to him by the late Queen on the morning of his 1986 wedding, after the long-running furore over his ties to convicted sex offender Epstein.

Charles is said to have acted, in consultation with William, Andrew and the royal family, on Friday after it emerged the then-duke had emailed Epstein in 2011 saying “we’re in this together”, three months after he claimed he had broken all contact with him.

The Mail On Sunday reported that Andrew embarked on a bid to smear Ms Giuffre.

He is said to have emailed the late Queen’s then-deputy press secretary and told him of his request to his protection officer, and also suggested Ms Giuffre had a criminal record.

The prince’s alleged attempt, on which the police officer is not said to have acted, came in 2011, hours before the newspaper first published the famous photograph of Andrew with his arm around Ms Giuffre in London.

The newspaper said it obtained the email from disclosures held by the US congress.

A Metropolitan Police spokesperson said: “We are aware of media reporting and are looking into the claims made.”

The prince was approached for comment.

Ms Giuffre’s posthumous memoirs, which are due out on Tuesday, have intensified the focus on the sexual assault allegations, which Andrew denies, and his links to Epstein.

Ms Giuffre wrote that Andrew insisted she sign a one-year gag order after their settlement to prevent tarnishing the late Queen’s Platinum Jubilee.

She described how Andrew’s disastrous Newsnight interview was like an “injection of jet fuel” for her legal team, and it raised the possibility of “subpoenaing” Sarah, Beatrice and Eugenie and drawing them into the legal case, The Telegraph reported.

Ms Giuffre said she got “more out of” Andrew than a reported 12 million US dollar pay out and two million dollar donation to her charity because she had “an acknowledgement that I and many other women had been victimised and a tacit pledge to never deny it again”.

The prince’s 2019 Newsnight interview, which he hoped would clear his name, backfired when he said he “did not regret” his friendship with convicted paedophile Epstein, who trafficked Ms Giuffre.

He was heavily criticised for failing to show sympathy with the sex offender’s victims.

Andrew also said he had “no recollection” of ever meeting Ms Giuffre and added he could not have had sex with her in March 2001 because he was at Pizza Express with Beatrice on the day in question.

Ms Giuffre alleged, which Andrew vehemently denies, that she was forced to have sex with the prince on three occasions, including when she was 17, after being trafficked by Epstein.

Queen Elizabeth II was celebrating her platinum jubilee in 2022 – the first British monarch to reach the milestone – as the civil case against her son gathered pace.

It was settled just nine days after she reached the 70th anniversary of her accession.

Ms Giuffre, who died by suicide in April, said in her book: “I agreed to a one-year gag order, which seemed important to the prince because it ensured that his mother’s platinum jubilee would not be tarnished any more than it already had been.”