Christie Elan-Cane, who does not identify as either male or female, believes Britain's passport application process is inappropriate.
At a hearing in London, High Court judge Andrew Gilbart granted the campaigner permission to bring a judicial review. A date for the challenge hearing has yet to be fixed.
"I am really elated but it is just one stage. There's still lots of work to do. We are not there yet," Elan-Cane told AFP after the hearing.
The campaigner claimed the British government was discriminating against its citizens in recognising gender- neutral passports held by citizens of other countries but not offering them to UK nationals.
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Elan-Cane's lawyer Kate Gallafent said her client considered that obtaining a passport would involve making a false declaration of gender identity.
The Passport Office's "refusal to provide for X passports affects not only non-gendered persons such as the claimant but a broad section of the public", she said.
Those affected included intersex people, transgendered individuals and people with gender dysphoria.
"The size of the potentially affected class is substantial; it has been estimated to be as high as one percent of the population," she said.
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