“There is a growing feeling that if you dislike the institution that much, you shouldn’t have the titles.”
Another royal insider said: “They should put the titles into abeyance, so they still exist, but are not used, like they agreed to do with their HRHs.
“They should just become Harry and Meghan. And if they refuse to do that, they have to explain why not.”
The remarks by the royal insiders suggest the Queen is under pressure to relinquish the royal couple of their titles.
As a result, he told the podcast host he stood down as a senior royal in an attempt to break the cycle of “pain and suffering”.
When asked if he was consciously trying to parent his son in a different way to his own upbringing, he said: “Yeah… Isn’t life about breaking the cycle?
“There’s no blame. But certainly when it comes to parenting, if I have experienced some kind of pain or suffering because of the pain or suffering that perhaps my father, or my parents had suffered, I’m going to make sure I break that cycle so I don’t pass it on.
“There is a lot of genetic pain and suffering that gets passed on anyway.
“As parents we should be doing the most that we can to say, ‘You know what, that happened to me, I’m gonna make sure that’s not going to happen to you’.”
The comments were a clear dig at his father, Prince Charles, and how he was brought up.
But as well as criticising the Prince of Wales, Harry also appeared to attack the Queen and Prince Philip’s parenting skills.
The Duke’s podcast appearances come just months after Meghan and Harry gave a tell-all interview with Oprah Winfrey.
During the two-hour programme, the couple accused an unnamed member of the Royal Family of racism and claimed the Firm failed to support Meghan when she was feeling suicidal.
As part of their Megxit agreement, Meghan and Harry agreed not to use their HRH titles.
However, they are still known as the Duke and Duchess of Sussex, and use the titles frequently.
Meghan has used the royal title on her debut children’s book, The Bench.