John Swinney will ask an incoming Labour government to lift the veto on Scotland’s Gender Recognition Reform Bill.

The First Minister said that while he thought that unlikely given recent comments from Sir Keir Starmer, he would seek to work “constructively” with the new administration on the issue.

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MSPs passed the Gender Recognition Reform Bill in 2022 by 86 votes to 39 on a cross-party basis.

The legislation aimed to speed up and simplify the process for a trans person to obtain a gender recognition certificate and change their legal sex.

Under the current system, this takes at least two years, involves a medical intervention and is only available at 18.

Holyrood’s Bill would have cut the waiting time to six months, lowered the age threshold to 16 and, crucially, scrapped the need for a doctor to diagnose gender dysphoria.

However, before it could become law, Scottish Secretary Alister Jack blocked it by using the first-ever order under Section 35 of the 1998 Scotland Act.

He argued that although the subject matter was within Holyrood’s powers, the Bill would have an adverse effect on the operation of UK-wide equality law, particularly sound single-sex protections.

The Scottish Government’s attempt to overturn the veto was rejected in the courts with ministers deciding not to appeal in December last year.

At the time, Shirley-Anne Somerville, the Cabinet Secretary for Social Justice told MSPs that the Bill would not be withdrawn and she was open to working with an incoming Labour government on the legislation.

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On Friday, Mr Swinney was asked by the BBC’s Good Morning Scotland if he would seek to work with a Labour government at Westminster to “lift the veto".

He replied: “I certainly will take that issue forward with the United Kingdom government.”

He added: “From what I have seen by way of public commentary from the Labour Party, they have indicated that is not something they would be prepared to take forward.

“What I want to say on this, I think it is an important point, I think it is important the public hear this in Scotland, is that their First Minister is interested in having a constructive relationship with the United Kingdom government.

“I always have done that as a minister and it’s been very difficult to have a constructive relationship with the United Kingdom Government in the last five years, because their behaviour has been so appalling.

“So I commit myself publicly to engaging with the United Kingdom government after the election and I hope we are in a position to take forward issues that matter to the people of Scotland.”

He also insisted: “I am absolutely wholly committed to protecting the safety of women and girls, and I give that commitment to women and girls in Scotland today.”

Asked directly if he would protect women’s rights to single-sex spaces from all males, regardless of whether they hold a gender recognition certificate, he replied: “Yes I would do that. I think that is provided for in the Equality Act 2010.

“But I think it is really important that the safety and security of women and girls is at the heart of our decision-making.”

Last week, during a visit to Whitburn, Sir Keir categorically refused to lift the block on the Scottish Government’s controversial gender reforms.

The Labour leader said there would “be no change of position on that” if his party formed the next UK Government.

“I think there’s a lot to learn about gender self-ID from the way in which it’s been dealt with here in Scotland, which is why we’ve got a different proposition in our manifesto.”

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On Thursday, Anas Sarwar was asked by the BBC if Labour would reopen discussions with the Scottish Government on the Bill.

He said: “Well, if a new piece of legislation comes forward it has to have the necessary safeguards, it has to respect the primacy of the Equality Act.”

Mr Sarwar, who backed the Holyrood legislation, added: “I want to remove the indignities of the process of obtaining a [gender recognition certificate] but we still have a lot of work to do to challenge sexism and misogyny and we have to protect these hard-fought rights — and that includes single-sex spaces based on biological sex.”

He said any new gender legislation “has to be road-tested to destruction” and has to take into account “those that may be bad faith actors”.

He said: “That’s not the trans community in general, it’s a community that faces prejudice every single day, and let’s be clear, since the passing of the GRR [Gender Recognition Reform] Bill our trans community feels no more protected and women feel no more reassured.

“We have got to address that really carefully, and so any legislation has to have the appropriate safeguards. There were amendments, for example, on prisons and sex offenders that were sadly rejected by the government, that we supported. I think that was a mistake.”

In its manifesto, Labour said it would “modernise” the process for obtaining a Gender Recognition Certificate. They would remove requirement to present evidence showing that a person has lived as their new gender for two years.

There would still be the need for a doctor to diagnose gender dysphoria.