Senior members of the Royal Family are said to be disappointed and hurt at the Duke and Duchess of Sussex's decision to step back from their current roles.
Prince Harry and Meghan did not inform the Queen or any other royal before their announcement on Wednesday, said BBC royal correspondent Jonny Dymond.
Buckingham Palace was "blindsided", he said, as talks about their future had begun but were in very early stages.
The Palace said there were "complicated issues" to work through.
Former BBC royal correspondent Peter Hunt told BBC Newsnight: "I'm always very wary of using the word 'unprecedented' but I cannot think of a previous example where they [the Royal Family] have washed their dirty linen in public."
In their statement, Harry and Meghan said they made the decision "after many months of reflection and internal discussions".
They plan to split their time between the UK and North America, while "continuing to honour our duty to the Queen, the Commonwealth, and our patronages".
"This geographic balance will enable us to raise our son with an appreciation for the royal tradition into which he was born, while also providing our family with the space to focus on the next chapter," the couple said.
Former press secretary to the Queen Dickie Arbiter said exactly how they will execute their plan "remains to be seen".
"It's is a logistical nightmare," he told Newsnight. "There's a question of security: who provides the security?
"Is it Scotland Yard, as it does provide royalty protection. Is it the Canadians that's going to be asked to provide it? Who is going to pay for it?"
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