Is Prince Andrew, the Duke of York, quietly being rehabilitated?

That was the speculation after he was photographed in a car with the Prince and Princess of Wales, on their way to a church service near Balmoral, on the Royal Family’s annual stay in Scotland.

The grainy photo of him in a Range Rover was seen as evidence of an olive branch being extended – the Royal Family subtly beginning the thawing process after he had been frozen out of public life.

But could that really be the case? After his connections with sex offender Jeffrey Epstein and the settlement following the civil court case with Virginia Giuffre, would the public accept seeing more of the Royal Family’s invisible man?

“People aren’t ready for his return,” says Anna Whitelock, royal commentator and professor of the history of modern monarchy at City, University of London.

King Charles is still trying to “establish his own identity as monarch”, she says, so bringing back Prince Andrew would be “very risky” in terms of public opinion.

The King should not allow his still relatively new reign to become defined by a row over bringing back Prince Andrew, she argues. “It would be wrong for this to be his biggest decision.”

In terms of family difficulties, Prof Whitelock believes the “priority should be repairing the relationship with Prince Harry”.

Prince Andrew might be keen to get back into royal duties, but Prof Whitelock says for the Royal Family, as an institution rather than as a family, there are only negatives.

And a well-placed source says that too much is being read into this car journey and that nothing has changed about the prince’s status.

He might attend a family event, but that is fundamentally different from carrying out royal duties.

Prince William has also been seen as being sensitive to such public appearances by Prince Andrew. It is understood that at last year’s Order of the Garter ceremony William threatened to pull out if Andrew was in the parade. The outcome – Andrew being out of view – was described as a “family decision”.

But for someone once known as Air Miles Andy, the Duke of York will not want to stay cooped up in Windsor forever, repeatedly photographed in his car, which must feel more like a merry-go-round.

So is there any way back?

Prince Andrew has always strongly denied any wrongdoing in the claims against him, but author and historian Sir Anthony Seldon says any comeback would require “remorse and contrition”.

“Without genuine and totally convincing humility, and satisfactory explanations for the past questions, a premature return could kill off his chances of a rehabilitation forever, and further damage the monarchy,” says Sir Anthony.

Gideon Benaim, head of the reputation protection team at law firm Simkins, says restoring Prince Andrew’s image would be a challenge.

“The public has clearly cast Prince Andrew into a bleak reputational pit and few are ready to consider or accept his rehabilitation,” says Mr Benaim.

“However, people also like to forgive. If, with the passage of time, they are provided with evidence of genuine contrition, humility and a sense that a person has learned the lessons of their own poor behaviour, they will tolerate rehabilitation,” says the solicitor and reputation expert.

The route back would mean “working for decades for the public good” and he gives the example of the 1960s politician John Profumo, who fell from grace after a sex scandal and then quietly did charity work for many years in London’s East End.

He ultimately restored his name, receiving a CBE from Queen Elizabeth in 1975.

But another royal insider, who wants to remain anonymous, does not believe that 63-year-old Prince Andrew is cut out to accept a life of humble charity work.

“Entitlement is the Achilles heel of the royals,” says this close observer, who also thinks Prince William made a mistake in putting his uncle in the front seat of his car when out in public.

“It was either naive or misjudged,” said the source, who believes that Andrew remains a restless figure, who will keep trying to get back into public life.

Part of the complication with stories about Prince Andrew is that so much is in the shadowlands of anonymous sources and unidentified “friends”.

As a non-working royal, Prince Andrew is not dealt with by palace spokespeople. Instead there is a swirl of unofficial comments and often contradictory rumour. Red herrings don’t get caught.

We hear nothing directly of the views of the man at the centre of all this. Instead, there are occasional glimpses, such as his ex-wife, Sarah Ferguson, talking about Andrew’s sense of loneliness at the loss of his parents.

The duke and duchess live together in Royal Lodge in Windsor, with a 75-year lease they are showing no sign of giving up. For a divorced couple they seem more married than most married people.

But there are some practical reasons not to expect any imminent return for Prince Andrew.

Royal advisers will be keenly aware of his ability to set off news landmines. What if further embarrassments emerge from US court cases about Jeffrey Epstein?

Or could there be more strange stories like when last year he was caught up in a legal case about a Turkish millionaire widow who had gifted him £750,000, which he then repaid?

There is also the unmistakable message of opinion polls. YouGov surveys show him as deeply unpopular with the public, most recently at -72 in favourability ratings.

As reputation lawyer Mr Benaim says, there would be a “mountain to climb” to bring him back in from the cold.