Nazanin Zaghari-Ratcliffe was arrested at Tehran Airport on April 3 while visiting family in Iran with daughter Gabriella.
The 38-year-old was imprisoned for five years last September and lost an appeal against her sentence in January but maintains her innocence.
She appealed to Iran’s Supreme Court where her sentence was upheld, and has been told there are no more legal avenues available, her husband Richard Ratcliffe said.
Speaking from the UK, Mr Ratcliffe vowed to continue putting pressure on the British Government, saying: “The solution now is political.”
He said: “If we got to a year and she wasn’t out I (said I) was going to start pushing again.
“We’ve had a year, the legal process is finished, so I think the Government needs to step up, find a way to visit her, say that she’s innocent and call for her release publicly.”
He added in a separate statement: “As her husband, I can say Nazanin is innocent until I am blue in the face. I have spent a year doing it. But it makes a clear difference that the government hasn’t. It indulges the whispers.”