Christie Elan-Cane, who was born female but identifies as "non-gendered", is pushing for a third option on passports for genderless people, which is usually symbolised by an 'x' on travel documents and birth certificates.
The case was brought before the Royal Courts of Justice on Wednesday and will now proceed to a full hearing, according to London-based law firm Clifford Chance, which has represented Elan-Cane since 2013.
"I couldn't quite believe it," Elan-Christie told the Thomson Reuters Foundation over the phone.
"It's really good news and I'm really pleased, but the work isn't over yet. There's much more work to be done."
It is the first legal challenge against the Home Office's (interior ministry) passport policy, Elan-Christie said.
"We are delighted that the Court has granted permission for a full hearing of this significant public interest case on the fundamentally important issue of the right to respect for individuals' identity," Narind Singh, a partner at Clifford Chance, said in a statement.
"X-passports are a crucial step in the protection of the human rights of this group of individuals."
A Home Office spokesman previously told the Thomson Reuters Foundation in an email "it would be inappropriate to comment on ongoing legal proceedings".
If Britain were to issue genderless passports, it would join Australia, New Zealand, Denmark, Germany, Malta, India, Nepal, Pakistan, Ireland and Canada.
(Reporting by Lin Taylor, Editing by Belinda Goldsmith and Katy Migiro. Thomson Reuters Foundation)