The UK Supreme Court has unanimously and unambiguously backed the argument that the definition of a woman in the Equality Act should be based on biological sex.

Reading out the ruling, Lord Hodge cautioned that it should not be taken as a triumph for one group in society over another.

But there were scenes of jubilation for women’s campaigners outside the Supreme Court.

Tearful hugs were exchanged and a bottle of champagne was cracked open.

The fact someone had thought to bring one along underlines that it was potentially on the cards, but For Women Scotland (FWS) still seemed shocked by the scale of their victory.

The Scottish government’s argument – that sex can be changed via the gender recognition process, and that someone with a gender recognition certificate should have the protections of that sex – were dismissed.

So what does it all mean?

The application of the law on the ground, in “real life”, was clearly foremost in the minds of the judges.

Take the example of single sex spaces and services – part of the motivation for FWS bringing this case.

The previous reading of the law was that everything from hospital wards and prison wings to support groups for victims of abuse can exclude everyone but women thanks to exceptions in the Equality Act.

The concern from campaigners was that if people could change their sex with a certificate, and then claim protection against discrimination as a woman, that could be more complicated.

That’s particularly the case on a practical level, given those providing these services aren’t actually meant to ask to see a gender recognition certificate.

Now, the court is clear that this exemption can continue – the rules underpinning women-only spaces can exclude people with gender recognition certificates, along with everyone else.

There are still conditions which need to be satisfied – services will have to show that excluding trans people is a limited and proportionate means to achieving a legitimate aim.

Blanket bans are generally discouraged. There is still a bar to clear to exclude anyone, and the test of proportionality has to be met in each case.

The Equality and Human Rights Commission – which oversees the application of the Equality Act – is to issue new guidance to help service providers

But FWS are clearly delighted with the underlying principle, and hope it will lead to clearer guidance for those providing services.

It’s important to note that trans people are still protected by the Equality Act.

The protected characteristic of gender reassignment is not affected by this ruling, and Lord Hodge stressed that there are other defences against direct and indirect discrimination and harassment.

He was clear that trans people are a “vulnerable and often harassed minority”, who “struggle against discrimination and prejudice as they seek to live their lives with dignity”.

But the court has held that it would be problematic to effectively divide trans people between two different protected characteristics, depending on whether they have a certificate.

Again, judges stressed that this is particularly the case when service providers can’t ask to see the certificate.

They say the law needs to be “clear and consistent” – and that including those with a GRC in with women would ultimately be “incoherent”.

The court carefully weighs the letter of the law, but it’s worth remembering that ultimately that law is drafted by politicians – and it can be changed at the stroke of a pen.

The issue may now move out of the legal arena and back into the political one.

There had been some pressure on the UK government to clarify the definitions of the Equality Act, which is Westminster legislation.

The court has handily done that for them, and UK ministers have welcomed the ruling.

There may be more political pressure on the Scottish government, given it has lost this case.

For a long time, ministers have batted away questions about this case – such as, do they really believe in the legal points their lawyers are making? – by saying they can’t comment on live litigation.

They will have to go into a little more detail now, but I imagine this is issue still just about the last thing they want to talk about.

There had been some speculation that a ruling like this could raise the prospect of ministers re-launching their attempts at gender reform at Holyrood.

But frankly there is not the political will in the John Swinney administration to ride into battle on this issue, as there was under his predecessor Nicola Sturgeon.

With a Holyrood election looming, there is no prospect of the first minister deciding to wade back into such a contentious debate.

But with For Women Scotland now hoping to use this ruling to hold his feet to fire when it comes to broader government policies and guidance, it is one he will need to address.