A couple who have been living together for the past six years will this week demand the right to a civil partnership, arguing that they face discrimination under the present law, which gives gay couples the option of marriage or a civil partnership but denies the latter to heterosexual couples.

Earlier this year the high court ruled against a legal challenge to the Civil Partnership Act 2004 by Rebecca Steinfeld and Charles Keidan. On Wednesday their appeal against that ruling will be heard in the high court, with judgment expected to be reserved. The couple say they are prepared to take their case to the supreme court and the European Court of Human Rights if necessary.

“A civil partnership would reflect who we are,” Keidan told the Observer. “It’s a modern social contract that doesn’t have the associations of marriage but would give the protection that we and other cohabiting couples crave.”

The act states that civil partnerships that provide legal rights and obligations to couples regarding children, property and pensions would be available to “two people of the same sex”. It was passed in 2004 in response to demands from gay rights campaigners for legal recognition for unions between same-sex couples. Then in 2013 same-sex marriage was legalised, giving gay couples the option of marriage or a civil partnership. The latter continues to be denied to heterosexual couples.

There are almost three million opposite sex couples living together in the UK, and almost four in 10 have dependent children, according to the Equal Civil Partnerships campaign. Although many people believe that people in “common law marriages” have rights over children and property protection, there is no such provision in law. “The fastest growing families in the UK are people who choose not to get married,” said Keidan, who has a 17-month-old daughter, Eden, with Steinfeld. “It would be a really straightforward thing for the government to extend civil partnerships to couples like us.”

Steinfeld added: “For many people, marriage is a very meaningful way to express their love. But there are also many reasons why people don’t want to get married. It’s not for the government to dictate, but to ensure that couples are legally protected.”

The couple have made wills, but will not have automatic rights to pensions or couples’ inheritance tax allowances. Their legal battle has been funded by their own savings, donations from philanthropic organisations and crowdfunding which raised £35,000. They are being represented in the court of appeal by lawyers acting on a pro bono basis.

At the high court hearing in January, the government argued that changing legislation would be “costly and complex”, and that following same-sex marriage legislation, civil partnerships may be phased out or abolished in the future. Following the ruling, a government spokesperson said that the “current regime of marriage and civil partnership does not disadvantage opposite sex couples”.

Steinfeld said it was untenable for the government to maintain the “unfair status quo”. The arguments regarding costs were shortsighted, she added. “The costs of changing the law pale into insignificance compared to the costs of dealing with the consequences of relationship breakdown where there is no legal protection.”

She and Keidan said there was growing support for a change in the law. More than 70,000 people have signed an online petition, and Conservative MP Tim Loughton has introduced a private member’s bill in parliament.

The only place in the British Isles where civil partnerships are available to different sex couples is the Isle of Man. After homosexuality was decriminalised on the island in the 1990s, a new law came into force earlier this year permitting marriage and civil partnerships to all couples.

Adeline Cosson and Kieran Hodgson became the first opposite-sex couple in the UK to enter into a civil partnership earlier this month, swiftly followed by Claire Beale and Martin Loat, who travelled from London for their ceremony. The Isle of Man is a crown dependency, but not part of the UK.After the new law was passed, Peter Tatchell, a campaigner for marriage equality, said: “Their new legislation is even more progressive than the UK. Instead of segregated marriage laws for gay and straight couples, they have a single civil marriage law that applies to everyone regardless of sexual orientation.

“The Isle of Man has also opened up civil partnerships to opposite-sex couples; in contrast to the ban that exists in England, Wales, Scotland and Northern Ireland. These changes catapult the Isle of Man to the forefront of legal equality for straight and gay couples.”