Sall Grover has taken her fight over women-only spaces to Australia's highest court after losing a landmark legal battle against a transgender woman who was removed from her female-only social networking app.

Grover and her company, Giggle for Girls Pty Ltd, confirmed on Monday that they had filed a special leave application with the High Court seeking to appeal a federal court decision handed down on May 15.

The High Court has accepted the filing of the special leave application. It has not yet publicly indicated whether special leave to appeal will be granted. 

The Giggle founder is seeking to overturn a ruling that found she unlawfully discriminated against transgender woman Roxanne Tickle when she excluded her from the women-only app.

Ms Grover has argued the judgment raises fundamental questions about the legal meaning of sex and the ability of women to create and maintain female-only spaces.

'This case is not just about one app or one individual. It is about whether women in Australia still have the right to single-sex spaces based on biological sex,' Grover said in a statement.

'These issues are of profound national importance. Reality and women's rights must be properly upheld in law.'

Ms Grover said the appeal seeks clarity on the interpretation of the Sex Discrimination Act 1984 and whether women-only services can lawfully restrict access on the basis of biological sex.

Ms Grover said she respects the judicial process but strongly disagrees with the court's conclusions.

'The judgment misinterprets the law, disregards biological reality, and sets a dangerous precedent that undermines women’s rights across Australia.

'This appeal to the High Court seeks definitive clarity on these issues of national importance and aims to safeguard the hard-won rights of women and girls to access single-sex spaces and services based on biological sex, not gender identity.'

Ms Tickle was rejected from the Giggle app in September 2021 after a selfie submitted to the platform led Ms Grover to conclude that she appeared to be male.

Under the Sex Discrimination Act, it is unlawful to discriminate against someone on the basis of their gender identity, sexual orientation or intersex status.

The appeal judgment also found that Ms Grover's conduct during the proceedings was 'gratuitous, disrespectful and unnecessary to the conduct of her case' after she referred to Ms Tickle using male pronouns.

Ms Tickle was born male but identifies as female. She has undergone gender-affirming surgery and hormone treatment and lives and works as a woman.

'They said I should call (Tickle) him only in private, not in public. Well, I'm sorry, the entire premise of the case is me saying Tickle is a man,' Ms Grover said.

'So, if I can't talk about the premise of the case ... then how is that justice? You may not agree with what I'm saying, but to punish someone for what their position is on the case I think is terrifying and sinister.'

Ms Grover has the support of Harry Potter author J.K. Rowling.

Following the federal court's decision, the court also doubled the damages awarded to the transgender woman, Roxanne Tickle, from $10,000 to $20,000. 

On top of that, the court ordered Ms Grover to pay Ms Tickle's legal costs of up to $100,000, which Ms Grover claimed demonstrated that Australia's judiciary is facing 'ideological capture'.