Harry and Meghan will be allowed to live independently and split their lives between Canada and the UK.
The Times said the “line of succession” photo upset the Duke and Duchess of Sussex.
Prince Andrew was absent from the family's traditional Christmas Day service.
The Duke of York is still expected to attend Trooping the Colour and Remembrance Sunday events in 2020.
The move would risk bringing the monarch deeper into the Brexit crisis.
The Prime Minister said the claims were "absolutely not" true.
The Queen approved the order on Wednesday afternoon to prorogue Parliament.
It hasn't always been a relaxing break for the Queen and her family.