Though he does not name the British Prime Minister Theresa May, it is clear that she and her "three Brexiteers" - Boris Johnson, David Davis and Liam Fox - are the targets of his attack.

In the paragraph of his email, Mr Rogers writes: "For my part, I hope that in my day-to-day dealings with you I have demonstrated the values which I have always espoused as a public servant. I hope you will continue to challenge ill-founded arguments and muddled thinking and that you will never be afraid to speak the truth to those in power. 

"I hope that you will support each other in those difficult moments where you have to deliver messages that are disagreeable to those who need to hear them. I hope that you will continue to be interested in the views of others, even where you disagree with them, and in understanding why others act and think in the way that they do.

"I hope that you will always provide the best advice and counsel you can to the politicians that our people have elected, and be proud of the essential role we play in the service of a great democracy."

The tone of his email suggests that Mr Rogers, a career diplomat who says he has served the last four Prime Ministers, has been involved in bitter clashes with Mrs May in recent months.

In the highly acclaimed All Out War, by Tim Shipman, it was revealed that Rogers clashed with Mr Cameron and members of his inner circle during last year's pre-referendum negotiations in Brussels.

"There is much we will not know until later this year"

In his email, Mr Rogers appears to show a lack of confidence in Mrs May's Brexit strategy, by questioning her plans to trigger Article 50 by the end of March this year.

Referring to her stubborn refusal to reveal her strategy to MPs, the public or even - it has been reported - the Queen, he writes: "We do not yet know what the Government will set as negotiating objectives for the UK's relationship with the EU after exit."

And referring to elections for a new French president and Angela Merkel's re-election bid in Germany, he continues:

"There is much we will not know until later this year about the political shape of the EU itself, and who the political protagonists in any negotiation with the UK will be."

In what will be seen by critics as a defence of his own lengthy experience and a suggestion that no-one else could do a better job, he writes: "Serious multilateral negotiating experience is in short supply in Whitehall, and that is not the case in the Commission or in the Council.

"The Government will only achieve the best for the country if it harnesses the best experience we have - a large proportion of which is concentrated in UKREP - and negotiates resolutely.  Senior Ministers, who will decide on our positions, issue by issue, also need from you detailed, unvarnished - even where this is uncomfortable - and nuanced understanding of the views, interests and incentives of the other 27."

He also hits out at senior ministers, particularly the UK's International Trade Secretary Liam Fox, who have suggested that the UK will enjoy a trade bonanza once it leaves the European Union.

"Contrary to the beliefs of some, free trade does not just happen when it is not thwarted by authorities: increasing market access to other markets and consumer choice in our own, depends on the deals, multilateral, pluri-lateral and bilateral that we strike, and the terms that we agree. I shall advise my successor to continue to make these points."

Responding to the email, Downing Street said it had nothing to add to an earlier statement, which said: "Sir Ivan Rogers has resigned a few months early as UK Permanent Representative to the European Union.  

"Sir Ivan has taken this decision now to enable a successor to be appointed before the UK invokes Article 50 by the end of March. We are grateful for his work and commitment over the last three years."

In a statement quoted by The New York Times, a European Commission spokesperson said: "We regret the loss of a very professional, very knowledgeable, while not always easy interlocutor and diplomat who always loyally defended the interests of his government."