Whitehall's most senior civil servant has ordered an inquiry into the leak of a UK Government account of a private meeting between Scottish National Party leader Nicola Sturgeon and the French ambassador.

The First Minister demanded the leak inquiry as she angrily denied claims that she told ambassador Sylvie Bermann that she would prefer to see Conservatives remain in power after the May 7 General Election.

The leaked memo was written by a Scotland Office civil servant following a conversation with consul-general Pierre-Alain Coffinier regarding the meeting between Ms Sturgeon and Ms Bermann, who was on her first visit to Scotland in February.

According to a copy published on the Daily Telegraph website, it said: "Discussion appears to have focused mainly on the political situation, with the FM stating that she wouldn't want a formal coalition with Labour; that the SNP would almost certainly have a large number of seats ... that she'd rather see David Cameron remain as PM."

Ms Sturgeon described the allegation as "100% untrue" and Ms Berman said she did not recall the first minster making such a statement.

A spokesman for Ms Bermann said: "While the Ambassador and First Minister, some time ago, discussed the political situation, Ms Sturgeon did not touch on her personal political preferences with regards to the future prime minister."

Attending an anti-nuclear rally in Glasgow today, Ms Sturgeon said: "This story has already been shown to be 100% untrue - having been comprehensively rejected by both the French Ambassador and Consul General.

"The real issue is how a second-hand and inaccurate account of this meeting - which was not even attended by the UK Government - came to be written by a UK Government civil servant and then leaked to Tory-supporting newspapers at the start of a General Election campaign.

"It suggests a Whitehall system out of control - a place where political dirty tricks are manufactured and leaked. And the Foreign Office now appears to be denying the very existence of such a document.

"I am therefore writing to the head of the UK civil service, Sir Jeremy Heywood, requesting an urgent inquiry into the circumstances of such a false account being leaked for transparently political motives.

"Anyone who knows anything about me knows I don't want to see a Conservative government. I'm campaigning to get the Tories out of Downing Street.

"We've made if very clear that we will lock David Cameron out of Downing Street - the only person who's not made that clear is Ed Miliband."

Sir Jeremy has responded to ms Sturgeon's request and says an inquiry is underway.

He said: "You have asked me to investigate issues relating to the apparent leak of a Scotland Office memo that forms the basis of this morning's Daily Telegraph story.

"I can confirm that earlier today I instigated a Cabinet Office-led leak inquiry to establish how extracts from this document may have got into the public domain. Until that inquiry is complete I will not be making any further comment either on the document or the inquiry."

Sir Jeremy is thought to be particularly concerned at the allegation of a leak because of the sensitivity of its timing, during one of the most finely balanced general elections of modern times.

Mr Miliband described the memo - written by a UK civil servant - as a "damning revelation" that the SNP was saying one thing in public and another in private, which he said made clear that the only way for Scottish voters to get the Conservatives out of office was to vote Labour.

The Labour leader again ruled out a formal coalition with the SNP, but declined to comment on the possibility of a looser agreement to co-operate if the election result is unconclusive.

A Labour spokesman added: "No-one will ever know for certain what went on between Nicola Sturgeon and the French ambassador. But what we do know is that the Tories are desperate for the SNP to do well, and the SNP are happy to see another Tory Government.

"The Tories know that the SNP are David Cameron's last hope of clinging on to power - and the Tories care a lot more about that than they do about the future of the United Kingdom.

"And we know the SNP care more about a second referendum than they do about stopping Tory austerity."

Scottish Liberal Democrat leader Willie Rennie said: "The First Minister might deny reports of her tete-a-tete with the French but we all know a Conservative-only government is the result of this election that the SNP want to see. A Tory PM governing alone in Downing Street and veering to the right fuels nationalist fires back home.

"Despite her fluffy, positive words about working with the rest of the UK we know what she really thinks. Her sole ambition is to break up the UK."

The Conservatives said it was a Labour and SNP alliance that had to be avoided.

David Cameron told Tory activists: "There is this coalition of chaos alliance we could end up with if we are not careful - an alliance between the people who want to bankrupt Britain - Labour - and the people who want to break up Britain - the SNP, Nicola Sturgeon and Alex Salmond. That's what we have got to avoid."