Prime Minister Boris Johnson is being urged to step down by many of his former allies
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Ms Donelan was only appointed on Tuesday evening but she has turned on the Prime Minister.
Mr Johnson has so far refused to accept that he has lost the trust of Conservative MPs but Ms Donelan joins a growing list of ministerial resignations.
She wrote: “It has been the privilege and honour of my life to serve for our country in the department which I believe is the most important, the true engine of opportunity, the Department of Education.
“I have spent my career dedicated to trying to create opportunities, or as I call it ‘opening doors’, to ensure that where you are from is no limit to where you end up. I have served on the Education Select Committee, as children and families minister, universities minister, higher and further education minister and most recently Secretary of State.
“Whilst I remain very worried about the prospect of no ministers in the department as we approach results day – the impact on students is real – as you know, yesterday I pleaded with you to do the right thing and resign for the sake of our country and our party; both are more important than any one person.
“In life we must always do what we believe is right. Above all I am here to serve the British public. I see no way that you can continue in post, but without a formal mechanism to remove you it seems that the only way that this is only possible is for those of us who remain in Cabinet to force your hand.
“You have put us in an impossible situation. I am deeply saddened that it has come to this, but as someone who values integrity above all else, I have no choice.
“I will continue to champion opportunity for our brilliantly talented and inspiring young people from the backbenches.”
Ms Donelan, 38, was appointed earlier this week to replace former Education Secretary Nadhim Zahawi.
Mr Zahawi himself was promoted to the position of Chancellor, after the dramatic resignation of Rishi Sunak – who followed ex-Health Secretary Sajid Javid out of the exit door two days ago.
Because of his refusal to resign, the Prime Minister faces the prospect of another confidence vote, orchestrated by the Tory 1922 Committee of backbench MPs.
A new executive for the committee will be elected next Monday and could change the leadership rules, allowing for another confidence vote just a month after the last one – which the Prime Minister is expected to lose given the way MPs have deserted him since Tuesday.