The couple want to get legal recognition for their relationship - but do not want to get married
The UK's court of appeal has ruled a heterosexual couple do not have the right to enter into a civil partnership.
Rebecca Steinfeld and Charles Keidan have been attempting to get legal recognition for their six-year relationship - but do not want to get married.
They have been stopped from getting a civil partnership as the law states they are only for same-sex couples.
In November they challenged a British High Court ruling against them, but this has now been dismissed by the Court of Appeal.
Speaking after the ruling Miss Steinfeld, 35, said they were "deeply disappointed" by the decision.
She said they had lost on a "technicality" and that "the government cannot maintain the status quo for much longer".
Mr Keidan, 40, said the couple was "determined to go on" with their appeal, taking the case to the UK's Supreme Court if the British government didn't act.
"Opening civil partnerships to all is fair, popular and will be good for families and children across the country," he said.
"There are over three million mixed sexed couples who are cohabiting, with two million dependent children. This is the fastest growing family type, but these couples lack legal and financial security."
The couple, who have a 20-month-old daughter, say that the British government's position is "incompatible with equality law".