William has previously stated that “change is on my agenda” when he ascends to the throne, and the couple have been in lockstep with the King’s decisions to distance the royal family from Andrew.
The King also issued a brief statement a few hours after Andrew’s arrest on Thursday, stating “the law must take its course”.
Public opinion is all-important, with the authority of the monarchy ultimately founded on the support and goodwill of ordinary men and women.
Broadcaster David Dimbleby, who recently presented the BBC documentary series What’s the Monarchy For? said about some members of the royal family: “Well they behave like people who are spoiled by entitlement.”
Speaking on BBC Radio 4’s World At One programme on Friday, he added: “Not all of them, Princess Anne, a paragon of virtue, wonderful, it’s not universal.
“But they’re lost in that world, nobody’s saying ‘come on pull yourselves together, do this, do that’.”
The events of the past few days could see MPs and peers formally discussing the issues around Andrew’s friendship with convicted paedophile Jeffrey Epstein.
Labour peer Lord Foulkes told the World at One: “I think there is now a clear expectation that there ought to be much more scrutiny.”
The politician said he has contacted MP Liam Byrne, chairman of the Business and Trade Commons Select Committee to “look” into Andrew’s work as a trade envoy but conceded it may be difficult now the police are investigating.