Video report by ITV News correspondent Dan Rivers
Iran has claimed the UK's move to grant diplomatic protection to Nazanin Zaghari-Ratcliffe is illegal.
Foreign Secretary Jeremy Hunt invoked the rarely-used diplomatic device in response to Iran's treatment of the dual national, who has been held since 2016 on spying charges.
Mr Hunt said he believed it was the first time such protection has been granted in more than 100 years.
But Tehran has refused to acknowledge the British-Iranian mother's dual nationality, arguing the UK's actions flout international law.
Mrs Zaghari-Ratcliffe's husband Richard described the move as a "big deal".
Explaining why he told ITV News: "Before Nazanin's case was an injustice that she was suffering and we were complaining about. The Government would have been sympathetic about.
"Now the Government is saying, 'listen we recognise this formally and we say this is a dispute we are taking forwards with Iran.'
"In terms of practically what it means, well then the UK has got more rights in terms of calling for protection of its citizens, it can demand to visit her more easily.
"Mr Hunt acknowledged that the move was unlikely to provide a "magic wand" solution, but insisted it sent a "very strong" message to the Iranian government."
"At the heart of this is an innocent woman, with a four-year-old daughter, who is very vulnerable, very scared and not well," Mr Hunt said.
"The right thing to do is to let her go and not use individuals as pawns of diplomatic leverage."
He added: "We have exhausted every other avenue. I have been to Iran, I've met the foreign minister on a number of occasions and I've spoken to him on the phone.
"I've asked them to recognise the human side of this dispute, but they have not done that and so we have taken this action."
Mr Ratcliffe said it would now be more difficult for Iran to turn down UK requests for visits to Mrs Zaghari-Ratcliffe in prison to check her condition.
He said his wife’s health was "obviously not in a great position, but I’m not sure how bad".
But hopes of a breakthrough were dealt a blow by Iran's ambassador to the UK Hamid Baeidinejad who rejected the Foreign Office announcement.
He said governments could only offer diplomatic protection for their own nationals and the UK was "acutely aware" that “Iran does not recognise dual nationality".
"Irrespective of UK residency, Ms Zaghari thus remains Iranian," he said.
Mr Hunt responded: "Well, I would expect some kind of negative reaction from Iran.
"All I would say to them is that we have really done everything possible."
Diplomatic protection is a mechanism in international law through which a state may seek reparation for injury to one of its nationals from an "internationally wrongful act" by another state.
Effectively it represents the right of states to raise the treatment of their nationals by other states and to call on them to account for their actions on the international stage.
It is distinct from diplomatic immunity, which covers the status of accredited diplomats.
While it does not automatically dictate any particular course of action, the Foreign Office has indicated it will take the steps it believes are most likely to secure the goal of Mrs Zaghari-Ratcliffe’s release.
Mrs Zaghari-Ratcliffe, a charity worker with the Thomson Reuters Foundation, was arrested in April 2016 at Tehran airport as she was returning home to London with her then 22-month-old daughter, Gabriella, following a family visit.
She was subsequently sentenced to five years’ imprisonment, despite strenuously denying the charges against her, while Gabriella remains in the country cared for by family.
Repeated calls for her release by the British Government – including a direct appeal by Theresa May to Iranian president Hassan Rouhani during last year’s UN general assembly in New York – have failed to produce results.
Mr Ratcliffe has previously said his wife was told by judges in court that her case related to an unpaid £400 million debt the UK owes to Iran in relation to the purchase of Chieftain tanks in the 1970s.
In January, she went on hunger strike for three days saying the Iranian prison authorities had refused her treatment for a series of medical conditions, including lumps in her breasts, severe neck pain, and numbness in her arms and legs.