Nazanin Zaghari-Ratcliffe was given a five-year jail term in September for participating in anti-regime protests in 2009.
After losing an initial appeal in January, Iran's Supreme Court upheld her sentence and Zaghari-Ratcliffe's family said they have been told there are no further legal avenues.
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Her husband Richard Ratcliffe said he will now seek a political solution to end the detention of his wife, who works for the Thomson Reuters Foundation which coordinates training programmes for journalists worldwide.
"We've had a year, the legal process is finished, so I think the (British) Government needs to step up, find a way to visit her, say that she's innocent and call for her release publicly," he told the Press Association.
The Foundation's CEO Monique Villa said Zaghari-Ratcliffe was not allowed to participate in her appeals, with the Supreme Court hearing held by a panel of judges.
"This extinguishes the last hope we have had of legally overturning a punishment where the crime remains a mystery," Villa said in a statement, explaining the exact charges remain unknown.
Zaghari-Ratcliffe was arrested at Tehran airport on April 3, 2016, after visiting family in Iran with her British-born daughter Gabriella.
Iran, which does not recognise dual-citizenship, confiscated the British passport of the two-year-old girl, who has been living with her grandparents in Iran since her mother's arrest.
Zaghari-Ratcliffe's husband said she was feeling "angry" but "determined" after losing her final appeal and is hoping for intervention from the UK.
Britain's foreign ministry said it was "deeply concerned" by reports the Supreme Court had upheld the sentence and said Prime Minister Theresa May and Foreign Minister Boris Johnson had raised the case with their Iranian counterparts.
"We continue to press the Iranians for access and for due process to be followed, and are ready to help get her daughter back safely to the UK if requested," a spokesperson said.
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Iran's elite Revolutionary Guards accused Zaghari-Ratcliffe of having taken part in the "sedition movement" of widespread protests that followed the 2009 re-election of former hardline president Mahmoud Ahmadinejad, charges which she denies.
During her detention Zaghari-Ratcliffe has suffered health problems and in November her husband said she had reached "breaking point", writing a suicide letter to him and her family.
After being held in solitary confinement, she was moved to the women's ward of Tehran's Evin prison on December 26 and has since received visits from her daughter.
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