Detained mother Nazanin Zaghari-Ratcliffe said it made her “heart melt” to have her seven-year-old daughter accept a bravery award on her behalf.
Gabriella read a speech written by her mother, who remains in Iran almost six years after her arrest and imprisonment.
Mrs Zaghari-Ratcliffe, a British-Iranian dual national, has been recognised at the Magnitsky Human Rights Awards.
Her husband, Richard, who recently spent 21 days on hunger strike to draw attention to his wife’s case, said the family was “very proud” of the honour.
Accepting the “courage under fire” award on her behalf at the event in London on Thursday evening, Gabriella read her mother’s words.
She said: “Thank you for this award. It means a lot to me and to my cellmates still in Evin Prison, that we are not forgotten.
“It makes my heart melt to see my daughter, now big enough to receive this award and to read these words.
“One day may we live in a world where we do not need to fight for our freedom. But thank you to all of you for walking next to us while we still need to do this fight, and for still reminding us that freedom is one day closer.”
Mrs Zaghari-Ratcliffe was arrested in Iran in 2016 as she prepared to fly back to the UK, having taken Gabriella – then not even two years old – to see relatives.
She remains in Iran at her parents’ home, with an appeal against her latest conviction having been rejected, and has always denied all charges against her.
A historic £400 million debt that Britain owes to Tehran – relating to a cancelled order for 1,500 Chieftain tanks dating back to the 1970s – has been linked to her detention, as well as that of other UK-Iranian dual nationals held in the country.
Speaking before the awards, Mr Ratcliffe said: “Nazanin was very pleased to hear of this award, for herself but also for all the others detained in Iran that you don’t get to hear about.
“The Iranian regime gets away with terrible crimes that thrive in darkness where accountability should be.”
So-called Magnitsky sanctions target those responsible for human rights violations or corruption.
Mr Ratcliffe added: “We are strengthened by the Global Magnitsky Justice Campaign’s recognition of that danger and the role of Magnitsky sanctions in challenging Iran’s state hostage-taking.
“All our family are very proud of this award.”
He told the PA news agency that the recognition was a “lovely surprise” for his wife, “knowing that other people care, and can see your injustice, knowing that you are not alone”.
He added that she was “a proud mum of her growing-up girl” .
Rupert Skilbeck, director of human rights organisation Redress, which has been part of the campaign to have Mrs Zaghari-Ratcliffe returned to the UK, said she had “endured intolerable suffering in Iran”.
He added: “This award is a timely reminder of the resilience and courage shown by many survivors of torture in the face of the most brutal human rights abuses.
“In recognising this, we must not forget that survivors deserve, and must receive, justice and reparation.
“The UK Government can and must impose Magnitsky sanctions on those responsible for Nazanin’s suffering.”
Bill Browder, head of the Global Magnitsky Justice Campaign and chief executive of Hermitage Capital Management, said: “Nazanin has bravely endured an unbelievable and unjust situation with grace and courage.
“Nobody should ever be put in a situation like this, but in spite of the pressure, she has proven how powerful she can be even in the most powerless situation.
“Her hostage-takers should understand that their crimes won’t go unpunished.”