Liberal Democrat MP Alistair Carmichael faces a legal bill of about £150,000 after a court ruled four constituents who unsuccessfully challenged his election are not liable for his costs.

The former Scottish secretary's bid for legal expenses, made after he survived an attempt to oust him from his Orkney and Shetland seat, was rejected by Election Court judges.

Lady Paton and Lord Matthews ruled in December the MP did not break electoral law by lying about a leaked memo ahead of the general election.

Mr Carmichael said: "Having won the case, this ruling is disappointing. However, the court has absolute discretion in these matters.

"We will now consider how these costs will be met. As has been the case since I was elected, my focus will remain serving the people of Orkney and Shetland at Parliament to the best of my ability."

Responding to the decision, Tim Morrison, one of the four petitioners in the case, said: "I am obviously relieved, intensely, and feeling vindicated."

The rare Election Court action was brought under Section 106 of the Representation of the People Act 1983.

This states that ''a person who ... before or during an election, for the purpose of affecting the return of any candidate at the election, makes or publishes any false statement of fact in relation to the candidate's personal character or conduct shall be guilty of an illegal practice''.

The judges found that while Mr Carmichael had told a ''blatant lie'' during a television interview about the leaked document, which wrongly claimed First Minister Nicola Sturgeon said she wanted David Cameron to remain in Downing Street, it had not been proven beyond reasonable doubt he had committed an ''illegal practice''.

The case centred on a Channel 4 interview on April 5 in which Mr Carmichael denied having prior knowledge of the memo leak, which emerged about a month before voters went to the polls.

Following a Cabinet Office inquiry, he later admitted he had allowed his special adviser Euan Roddin to release details of the document, which appeared in the Daily Telegraph on April 3.

Roddy Dunlop QC, acting for Mr Carmichael, had argued "expenses should follow success" after the legal challenge was dismissed.

He said it was "frankly inconceivable" that if the four petitioners had succeeded, they would not have sought expenses against the MP.

Jonathan Mitchell QC, for the petitioners, told the court there had been a public interest in bringing the case and pointed out they had successfully argued several points.

He said: "This is not a petition brought frivolously or vexatiously, and indeed Mr Dunlop has not suggested that it was.

"It would simply not be just if the petitioners, having brought this case, having got the public to support them, as to a limited extent the respondent has, should then be told that they have to pay the expenses of his uncandid defence."

After hearing the legal arguments, Lady Paton said: "In all the circumstances, exercising our discretion, we consider this to be in effect a case with divided success.

"Accordingly, we find no expenses due to or by any party."

The petitioners have raised almost £210,000 towards their legal fees via a crowdfunding appeal while a separate crowdfunder set up by a friend of Mr Carmichael has raised more than £14,500 towards his expenses.