Rebecca Steinfeld and Charles Keidan are about to become parents. They wish to formalise their union. Both describe themselves as feminists and reject traditional, “patriarchal” marriage.

This month the couple, both academics, have launched a legal challenge against the ban on members of the opposite sex entering into civil partnerships – a development the prime minister, David Cameron, has condemned as likely to undermine the institution of marriage.

Their test case is believed to be the first attempt in the British courts to make partnerships available to heterosexual people. The 2004 Civil Partnership Act stipulates that only same-sex couples are eligible. The couple believe it is unfair to prevent them enjoying the status.

The legal initiative coincides with a debate due in parliament later this week on a private member’s bill sponsored by Tim Loughton, the former Conservative children’s minister, also aimed at removing the words “same sex” from the 2004 act.

Steinfeld and Keidan have already tried to hold the ceremony. In October, they arrived at Chelsea Town Hall registry office. “The registrar was very sympathetic but confirmed we were of the opposite sex and said consequently she could not provide a civil partnership,” explained Steinfeld, 33, who was until recently a visiting scholar at Stanford University in the US. “I asked if she would consider an act of civil disobedience. She said: ‘It’s not worth my job.’”

The couple’s lawyers have now served notice of their intention to launch a judicial review on the local council, Kensington and Chelsea, as well as the secretary of state for culture, media and sport, Sajid Javid.

The couple first met at a London School of Economics lecture in 2010 and become engaged last year. “We put a notice in the Jewish Chronicle,” said Keidan, 38, who is a research fellow at City University’s Cass business school. “We asked them to create a special section in the social pages for ‘forthcoming civil partnerships’.”

They believe marriage represents a malign past. “We see ourselves as partners,” Steinfeld said, “and we are seeking a social institution that will express how we see each other. In terms of giving us legal rights and responsibilities, a civil partnership is almost identical to marriage.

“Our objection to marriage is partly to do with its history, a union in which women were exploited for their domestic and sexual services. There are still sexist trappings to weddings: there’s only space for the father to sign on the registry form.”

Keidan added: “It’s almost about the social expectations of marriage: the father giving away his daughter to the groom, hen and stag events, the virginal white dresses. That’s not the type of relationship we want.”

They point out that some countries have already opened up civil partnerships to everyone. “The perception may be that opening up civil partnerships is a threat to marriage but in the Netherlands both institutions [co-exist],” said Steinfeld. “A survey in 2009 showed that nearly 90% of couples were choosing marriage. We hope that civil partnerships will draw their support from long-term cohabiting couples.”

The couple, who are expecting their first child next year, are hoping to attract crowd funding for their legal action from those who support equal unions. Their legal claim has been drawn up by Louise Whitfield, a solicitor at the law firm Deighton Pierce Glynn. She said: “This is a very important case in relation to equality, not only for heterosexual couples wishing to enter civil partnerships but to reinforce equality for women in terms of the institutions available for recognising long-term relationships.”