Mr Jephson compared the actions of the couple to those of the Queen, and the Duke and Duchess of Cambridge, in responding to the coronavirus crisis. The royal couple are currently living in Meghan’s home town of Los Angeles with their son.
Writing in the Mail on Sunday Mr Jephson said: “Common sense – and decency – would compel the Sussexes to hunker down with their baby in the temporary comfort of a borrowed mansion and hope the rest of us wouldn’t notice their period of wise invisibility.
“But they dare not, because to be invisible and un-royal now is to fail the audition. And that, they simply can’t afford.
“If we wish them success in their new adventure in the world’s entertainment capital, we must help them cast off ties to the institution and country they seem to think they’ve outgrown.
“Now, surely, is the time to unburden them from the stress of being half-celebrity, half-toxic Royal.
“Their attempts to ride on the coat-tails of the hard-working family they have abandoned do nobody any good.
“In April 2020, real royalty isn’t Instagramming from Malibu but working here, among crowded hospitals and deserted streets.
“This is where historic Royal titles are earned and re-earned, and this is where Harry and Meghan must leave theirs. For their own good – and for the good of the Crown they claim to serve.”
Meghan and Harry shocked the world in January by announcing they were stepping down as senior members of the royal family and would seek to become “financially independent”.
The couple officially ended their senior royal duties at the end of March.
They moved first to Canada, then to Los Angeles where Meghan was born and brought up.
Meghan and Harry agreed to drop their ‘Sussex Royal’ brand after talks with the wider royal family.
They have also pledged to repay the taxpayer money spent renovating Frogmore Cottage, their former home near Windsor.
Mr Jephson contrasted the response of Meghan and Harry to the UK coronavirus outbreak with that of other royals.
He said: “It may have been years since the Royal Family had a real chance to do their job as the heart and soul of the kingdom but by God and by the grace of Covid they have it now.
“Never in living memory (for most of her subjects) has the Queen better embodied the modest optimism and quiet resolve that define the best of British character.
“Her family in turn have played their part to justified acclaim, none more applauded than the relatable, telegenic and just plain decent Cambridges.
“It seems an age ago that Meghan and Harry joined William and Catherine to form the ‘Fab Four’ of young Royal stars, whose charisma, approachability and fundraising potential seemed limitless.”
Meghan and Harry have been spotted out in LA several times delivering food to vulnerable people since the coronavirus crisis began.
Earlier this month, appearing on the Declassified podcast, Prince Harry praised the UK public’s reaction to the crisis.
He said: “It’s such a wonderfully British thing that we all come to help when we need it.
“It makes me incredibly proud to see the Brits stepping up like this.
“I really hope this keeps going after coronavirus.”