The plan has drawn criticism by leading Brexiteer Jacob Rees-Mogg, who described it as a "wartime fantasy", the Mail on Sunday reported.
"The over-excited officials who have dreamt up this nonsense are clearly more students of fantasy than of history," Rees-Mogg said.
"The Monarch's place is always in the capital, as the late Queen Mother, wife of George VI, made very clear during the Blitz.'
A source in the Secretariat said that the most extreme No Deal crisis scenario envisaged riots breaking out in London as shops ran short of staple foods.
The source claimed that the plan had been moved up their "priority list".
The source said: "As the Queen has been dragged into some of the politics around all this, it becomes more likely that she and her family could be targeted by protesters."
Neither Buckingham Palace nor Downing Street would comment yesterday, citing security concerns, but a senior Government source said: "It is not project fear. There are dozens of contingency planners whose job is to envisage every possible eventuality. They would be negligent if they didn't include the Royals in that, however far-fetched the scenario might seem."