Ms Steinfeld and Mr Keidan said the civil partnership, which came into law for same-sex couples in 2005, “captures the essence of our relationship and values”.
They view the arrangement as a “simple, modern contract conferring almost identical rights and responsibilities as marriage”, but without its social pressures.
Mr Keidan said: “Over the last few years, we’ve heard the same message: whilst most couples want financial and legal protection for themselves and their families, not all feel comfortable with marriage.
“Civil partnerships offer a legally binding arrangement that is fair, popular and good for families and children.”
Ms Steinfeld added: “We hope the Supreme Court will deliver a judgment that will finally provide access to civil partnerships for thousands of families across the country.”
The couple’s case was first rejected by the High Court in January 2016, and the Court of Appeal later said there was a potential breach of their human rights.
Two of the judges said the government should be allowed more time to make a decision on whether to extend civil partnerships to mixed-sex couples.
Their solicitor, Louise Whitfield, said bringing the case to the Supreme Court, which hears a small number of cases each year, was a “significant achievement”.
Their case is expected to be heard in the first half of 2018.
