Labour are not the only party to have tied themselves in knots on this issue.
It was particularly thorny for the SNP, whose former leader Nicola Sturgeon championed the expansion of trans rights, cheered on by some in her party and opposed loudly by others.
Scotland's First Minister John Swinney, who has been keen to avoid the issue, will now face the challenge of ensuring his government adheres to the law as interpreted by the Supreme Court.
The Liberal Democrats have had their problems too.
Officially, the party is pro-trans rights. It has a powerful and influential LGBTQ+ section and campaigned at the last general election for legal recognition of non-binary identities.
In May 2023, leader Sir Ed Davey told LBC: "The vast majority of people will have the same gender as their biological sex, but a small number won't."
When asked by presenter Nick Ferrari "so, a woman can have a penis?", he replied: "Well, quite clearly."
He went on to suggest that trans people's rights were adequately protected by the Equality Act, which "allow there to be single sex spaces".
His comments were ridiculed by then Tory leader Sunak – and did not go down well with gender critical campaigners in his own party.
Liberal Voice for Women (LVW), which has fought a long campaign against a ban on having a stall at the annual Lib Dem conference, said their leader had made the party "look dishonest, unreliable and detached from reality".
Earlier this year, party chiefs backed down and allowed LVW to hold events and have exhibition stands after the group threatened to sue for discrimination.
Reform UK is clear in its opposition to what it calls "transgender indoctrination" and is committed to scrapping the Equality Act.
Its 2024 general election "contract" states: "There are two sexes and two genders."
The party adds: "It is a dangerous safeguarding issue to confuse children by suggesting otherwise… no gender questioning, social transitioning or pronoun swapping, inform parents of under-16s about their children's life decisions. Schools must have single-sex facilities."
On paper, the Green Party of England and Wales is equally clear, at the opposite end of the spectrum.
The party's charter of Rights and Responsibilities states "trans men are men, trans women are women, and that non-binary identities exist and are valid", and it campaigns to make it easier for trans people to change their legal status.
But within the party there are major splits over the issue.
Last year, the Greens were ordered by a court to pay nearly £100,000 to their former deputy leader Shahrar Ali after it found the party had discriminated against him when they fired him as a spokesman during a row over his gender critical beliefs.
Today's court ruling takes the immediate pressure off the Labour government and other politicians who have struggled to answer the question "what is a woman?"
But with passions running high on both sides of the debate, it is unlikely to go away.
Additional reporting by Sam Francis and James Cook