Two Green party members who hoped to stand for parliament on a job share basis have been refused permission to challenge their rejection in the high court.

Sarah Cope and Clare Phipps submitted joint nomination papers for the general election in May, but their combined candidacy was ruled as invalid by the returning officer in the constituency of Basingstoke.

The pair, whose legal application was supported by their party and paid for with crowdfunding, believe there should be more women in parliament. But the judge hearing the case, Mr Justice Wilkie, turned down their application to launch a full-scale judicial review of the returning officer’s decision. It had been “unarguably correct”, the judge said. The two women could still appeal against the high court ruling.

Cope is the main carer for two young children and Phipps has a disability. They maintained that they could have represented the constituency better by combining their efforts. Their claim, drawn up by solicitors Leigh Day, said preventing the two women from jointly working as an MP amounted to a disproportionate and unjustifiable interference with both the Human Rights Act and the Equality Act.

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Cope, 36, has been an active member of the Green party for more than a decade and chairs the Green party women sub-group. She has developed many of the Greens’ policy areas, including those on maternity services, breastfeeding, childcare and prison reform.

She said: “The 32 million UK women make up 51% of the population. At the moment, however, over 450 of the 650 MPs in parliament are men. We need to change the culture of Westminster and stop wasting so much untapped talent. Allowing MPs to job share is a relatively minor change which could bring about huge benefits.”

Phipps, 26, is researching gender and health in a part-time PhD and job shares a position on the Green party executive. Since 2009, she has suffered from a disability known as idiopathic hypersomnia, a chronic condition that means she sleeps for about 12 hours a day.

She said: “The concept of job shares has been accepted for some time now, and in a wide array of fields – from doctors, to teachers, to judges. It is essential that we bring parliament up to speed with the rest of society by allowing MPs to job share.

“Allowing those currently barred due to health conditions or caring and family responsibilities to become MPs would not only give these people their fundamental right to participate in our democracy, it would allow them to fight from within the House of Commons against policies which currently see the privileged few gain at the expense of the most vulnerable in our society.”

In 2010, the Green MP Caroline Lucas told her annual party conference: “I’d like to see the law changed to allow candidates for parliament to stand as job shares. Nothing would do more to open up politics to women. Now I know the establishment will pour scorn on the idea and say it’s ideas like that which make us unelectable. Fine. Let them. But I also know that this, too, is an idea whose time will come.”