The Channel 4 episode followed Lord Mountbatten as he acted as Charles’ kingmaker and matchmaker.
In a photo album filmed for the first time on television, the woman who turned down Charles’ marriage proposal was revealed.
The University of Southampton’s special collections archive now houses Mountbatten’s private family photograph albums.
Channel 4 said: “But one special album, never before filmed for television revealed Mountbatten’s choice for the future queen of England. His own granddaughter.
“His granddaughter Amanda Knatchbull was the perfect candidate and was the right age. The two of them got on really well.
“Amanda was Charles’ cousin. These intimate photos taken on the Caribbean island of Eleuthera in 1977. For years, Mountbatten was secretly lining Amanda up as a future queen.”
One royal commentator admitted: “He was manoeuvring the prince away from Camilla, saying ‘If you carry on with her, you’re going to end up like David! People will hate you and your reputation will just disappear. So why don’t you give her up and go for my granddaughter?’.
In the summer of 1979, Charles and Amanda were due to holiday together, the programme explained.
The voiceover continued: “Amanda gets on the Royal Yacht Britannia and they sail off to the Western Isles. During that period Charles turns to her and says, ‘Will you be my wife?’ and she says no.”
“They’d been together a lot, and I think that actually the relationship was too close. They were like brother and sister,” added another royal commentator.
“Charles had tried to do his duty and follow the advice of his mentor. It seemed the crisis over his future could’t get any worse.”
The revelation comes after last week’s episode revealed how Prince Philip was the Windsors’ most radical moderniser, and how in the 1960s he harnessed the medium of television to revamp the royals’ public image
Next week’s continuation will examine the huge challenge that Diana’s popularity and tragic death posed to the royal family.
The Royal House of Windsor continues on Channel 4 next Wednesday at 9pm.