Former Scottish secretary Alistair Carmichael has apologised to both Nicola Sturgeon and the French ambassador to the UK after accepting responsibility for a leaked memo which alleged the Scotland First Minister wanted Tory leader David Cameron to win the general election.

Liberal Democrat Mr Carmichael conceded he should not have agreed to the document being made public by his special adviser, Euan Roddin.

Cabinet Secretary Sir Jeremy Heywood ordered an inquiry into how the note, which claimed that Ms Sturgeon told ambassador Sylvie Bermann that she would prefer to see Conservatives remain in

power after the general election, got into the public domain.

The Cabinet Office investigation concluded that Mr Carmichael "could and should have stopped the sharing of the memo" and added that he "accepts responsibility for what occurred".

Mr Carmichael, who is now Scotland's only Lib Dem MP after the party lost 10 of its 11 seats north of the border, said that, while he had not seen the document before it was published by the Daily

Telegraph, he was "aware of its content and agreed that my special adviser should make it public".

He stated: "I should not have agreed this. It was an error of judgment which I regret.

"I accept full responsibility for the publication of the document.

"I have written today to the First Minister and to the French Ambassador to apologise to them both."

Mr Carmichael added: "Had I still been a government minister, I would have considered this to be a matter that required my resignation. I have therefore informed the Cabinet Secretary that I will decline my ministerial severance payment."

First Minister Nicola Sturgeon said: "I am satisfied that Sir Jeremy Heywood has established the truth about this sorry matter, and I thank him for his work.

"Alistair Carmichael has written to me accepting that the account of my conversation with the French Ambassador was not correct, and apologising for what was a blatant election dirty trick in having it leaked.

"I accept his apology, but the real issue is that he should be apologising to the people of Orkney and Shetland, because he clearly contested the election on false pretences.

"Mr Carmichael said at the time that the first he was aware of this matter was when he received a call from a journalist, but we now know that this is simply untrue. The false memo was leaked by a Special Adviser acting under the authority of Mr Carmichael. He knew all about it, but said in public that he knew nothing until a journalist phoned him.

"As well as the original dirty trick, which was bad enough, Mr Carmichael then tried to cover it up - and is only admitting it now because he got caught.

"He needs to seriously reflect on that - and reflect on whether his actions and attempt to cover them up are consistent with his position as an honourable member of the House of Commons."