NICOLA Sturgeon is facing cross-party calls to explain how her government cost taxpayers £500,000 by bungling the sexual misconduct investigation into her predecessor.

The Scottish Conservatives called for a Holyrood inquiry after the high-profile probe into Alex Salmond collapsed after being exposed as fundamentally unfair.

Scottish Labour also wrote to Ms Sturgeon demanding she set out the full details of her contacts with Mr Salmond during the course of the seven-month inquiry.

The calls add to the pressure on Ms Sturgeon, who is expected to face intense scrutiny at First Minister’s Questions today.

The Tories want one of Holyrood’s committees, potentially the Public Audit Committee as it follows the public pound and has an SNP minority, to examine the background to the case.

Acting Scottish Tory leader Jackson Carlaw said: “The two women at the centre of this case have been failed by the Scottish Government. And when £500,000 of public money has been squandered in the process, the public is entitled to answers.

“If the SNP government won’t front up, then the Scottish Parliament will need to do so. A Holyrood inquiry to find out what went on here may be the only way forward.”

Scottish Secretary David Mundell added: “It’s a matter of concern that the Scottish Government did not have procedures in place so people, who had issues they wanted to raise in relation to serious allegations, [felt] they could be robustly defended.”

The relationship between Ms Sturgeon and Mr Salmond hit rock bottom on Tuesday after the former First Minister won his judicial review case at the Court of Session.

He had challenged how the Scottish Government and its top official, Permanent Secretary Leslie Evans, had handled an inquiry into two sexual misconduct complaints against him.

Two women alleged in January 2018 that he behaved inappropriately towards them while he was First Minister five years earlier.

Mr Salmond, 64, who denies harassment or criminality, took the government he once led to court after the existence of the investigation became public last August in a leak.

After he forced the government to hand over hundreds of previously secret documents in December, it emerged the investigating officer assigned to the case had been in prior contact with his accusers, rendering the resulting process unlawful, procedurally unfair and “tainted by apparent bias”.

After Mr Salmond said Ms Evans should quit, Ms Sturgeon publicly backed her.

Although the First Minister was not meant to know about the investigation while it was ongoing, Mr Salmond told her about it himself last April at her home.

She then granted him two more face-to-face meetings in June and July, and two telephone calls in April and July, in which he continued to carp about the process.

Ms Sturgeon told Holyrood on Tuesday that she was “always clear” with her mentor that she had no role in the investigation.

“I did not seek to intervene in it an any stage - nor, indeed, did I feel under pressure to do so,” she said, prompting MSPs to question why she’d talked to him at all about it.

In her letter to the FM, Labour MSP Pauline McNeil said the government’s mistake would cause “deep distress” to the women who complained about Mr Salmond.

She said: “It is quite devastating for others to see the Scottish Government, with all the resource at its disposal, couldn’t get this right.

“These women, and the public, will have expected at the very least a competent investigation into these most serious of matters. They have been badly let down by your administration.”

She said it was “not credible” none of Ms Sturgeon’s contacts with Mr Salmond were in her published diary, and said they could have “compromised” the investigation.

There were also questions about the timing of the government’s climbdown.

Ms Sturgeon signed off Ms Evans’s decision to throw in the towel last Thursday, four days before two of the First Minister’s closest aides were due in court.

The FM’s chief of staff Liz Lloyd and Principal Private Secretary John Somers had been due to testify on Monday about the hitherto secret documents.

The government admitted defeat just hours after being told that Mr Salmond’s side was insisting Ms Lloyd and Mr Somers would have to be questioned under oath.

Mr Carlaw said: “It begs the question: did the Government cave in to stop more facts coming to light about its involvement?”

The government said the decision was “entirely unconnected” to the court date.

Meanwhile, it was emerged SNP Westminster leader Ian Blackford has cold-shouldered Mr Salmond since August.

The Skye MP said: “I haven’t spoken to Alex Salmond for a considerable period of time. There is a process that has to be gone through and a police inquiry to take place. What comes after that will be determined by the police inquiry.”

However Mr Salmond remains close to a number of Mr Blackford’s MPs, including Angus MacNeil and Joanna Cherry QC.

A Government spokesperson said: “The First Minister, the Permanent Secretary and the Government’s legal team have already set out the reasons for settling this case, which specifically relate to contact between the Investigating Officer and the complainants around the time of the complaints being made in January 2018.

“Any other claims or conspiracy theories are ridiculous and unfounded.

“The First Minister has set out the details of her meetings and phone calls with Alex Salmond and the substance of them. Mr Salmond initially told the First Minister of the investigation and complaints against him in April 2018. In subsequent meetings and phone calls he raised his concerns about elements of the process and informed the First Minister that he was proposing mediation and arbitration. As the First Minister told Parliament, she was clear to Mr Salmond that she had no role in the process and would not intervene.”