A leaked civil service memo which alleged the Scottish First Minister Nicola Sturgeon wanted David Cameron to win the general election was an “accurate” record of a conversation with a French official, an investigation has concluded.

The former Scottish Secretary Alistair Carmichael admitted he had agreed to leak the memo to a newspaper during the election campaign after his involvement was exposed by a Cabinet Office inquiry. But, significantly, the inquiry concluded that the memo itself was genuine and “an accurate record of the conversation that took place between him (the civil servant) and the French Consul General”.

The note claimed that Ms Sturgeon told French ambassador Sylvie Bermann that she would prefer to see the Conservatives remain in power and that Ed Miliband was not “prime minister material”.

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 [Euan Roddin] should make it public”.

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