A teenage Princess Anne, played by Erin Doherty, was introduced in the most recent series, boasting a near-constant smirk and a regularly raised eyebrow.
"So many people asked me, after she first appeared, to put more of her in there," Morgan said.
"Anne's often overlooked.
"But Erin's portrayal means that everybody has fallen in love with her. Searches about her on Google went through the roof, she's now one of the most popular royals."
Anne might well raise an eyebrow at the very thought.
She recently revealed that she did watch early episodes of the show, which she found "quite interesting".
She has also laughed at revelations that it sometimes took two hours to get Doherty's hair into the requisite style.
"I read an article the other day about The Crown, the actress was talking about how long it took them to do their hair like I did," she told ITV's Anne: The Princess Royal at 70.
"And I'm thinking, 'How could you possibly take that long?' I mean it takes me 10 or 15 minutes."
The fourth series of The Crown, due to be released later this year, will see the introduction of a young Princess Diana, played by Cambridge-educated actress Emma Corrin, 24.
It will depict the transition of Diana from her early days as a shy kindergarten teaching assistant to a global figure, as well exploring the early days of her disastrous marriage to Prince Charles.
One episode, set in New York but filmed largely in Manchester, explores Princess Diana's first solo tour of the city in 1989, which the American media fawned over.
Another episode will focus on Charles and Diana's tour of Australia in 1983.
In the final two series of the show, Australian actress Elizabeth Debicki will take on the role of Diana.
Corrin, who spent more than two hours a day in the make-up chair, said she had never been told she looks like Princess Diana before. She told the Mail on Sunday: "I have never had that. I get told I look like a young Jodie Foster."
The brief for the part called for "a mesmerising new young star with extraordinary range", adding: "She has to play charming comedy, flirt and social exhibitionist on the world stage, desperate and lonely self-harmer at her lowest ebb and the kind of psychological intensity of Mia Farrow in Rosemary's Baby."
Corrin was offered the part in person at the final audition. She said: "It felt like I'd just been proposed to; it was the best moment of my life.
"There's a lot of pressure, but I've been glued to the show since the first episode and to think I'm now joining this incredibly talented acting family is just surreal."
The actress was given a bundle of written material and documentaries to watch and spent hours perfecting the princess's distinctive voice with a vocal coach and emulating her mannerisms.
"Something they have been making clear from the start is that this is not an impression," she said.
"I am going for essence. Any movement and voice work we have done has been figuring out why she talks the way she does, and how she was a massive departure from the Royal Family, a bit like Meghan is now I guess, by bringing something different in the way she talks."
The series will also see the introduction of Margaret Thatcher, played by Gillian Anderson.
