Campaigners hope "disturbing" findings about Iran's human rights record will "jolt" the UK Government into doing more to free British-Iranians jailed in Tehran.
Foreign Office minister Alistair Burt is visiting Iran this week and is expected to raise the cases of dual national detainees including Nazanin Zaghari-Ratcliffe and 77-year-old grandfather Kamal Foroughi.
Both were imprisoned for alleged crimes they have denied
Tory MP Mr Burt said he wants to make "progress" in several areas, including on the dual national detainees, when he meets senior Iranian politicians during his two-day visit which begins on Friday.
But Amnesty International UK says a new report highlighting fresh human rights concerns should stop UK officials making "vague remarks" and instead prompt them to speak "loud and clear" about the need to free Ms Zaghari-Ratcliffe and Mr Foroughi.
Pressure has been increasing on Foreign Secretary Boris Johnson and Prime Minister Theresa May to do more, with Tory MPs among those who used a parliamentary debate last month to call for firm action.
Ms Zaghari-Ratcliffe was arrested at Tehran Airport last year while visiting family with daughter Gabriella.
She was jailed for allegedly plotting to topple the Iranian government - a charge she has repeatedly denied.
Mr Foroughi is held in the same jail for alleged espionage in Iran but has strenuously maintained his innocence.
The Foreign Office says it has been denied consular access to check on the welfare of those detained as Iran does not recognise dual nationality.
It has added it continues to lobby Iranian authorities about the cases at the "highest levels at every opportunity".
Amnesty International's report, "Caught in a web of repression - Iran's human rights defenders under attack", claims there have been "suffocating levels of repression" through the country's judiciary and security services since Hassan Rouhani became president in 2013.
The group warns of unfair trials, prison sentences of more than 10 years given to human rights activists, and people being accused of national security offences for protesting against issues such as the death penalty.
Lucy Wake, Amnesty International UK's government and political relations manager, said: "Iran is in the midst of a vicious and widespread crackdown on human rights activists, and this report is a frightening insight into Nazanin's and Kamal's plight.
"From prolonged periods of solitary confinement after arrest, to secretive and unfair trials and the use of bogus 'national security' charges, the way the authorities have treated Iran's beleaguered human rights activists is strikingly similar to how they've treated Nazanin and Kamal.
"We're urging Foreign Office officials to study this disturbing report in detail as it provides a chilling insight into the way Iran's judiciary and security apparatus are systematically abusing human rights.
"The report should jolt the UK Government out of its complacency over Nazanin's and Kamal's cases.
"Instead of vague remarks about 'raising' Nazanin's plight with Iran, the UK needs to say loud and clear that her continuing detention is illegal under international law and she should be released immediately.
"Similarly, the UK should redouble its efforts to secure Kamal's long-overdue release."
MPs heard last month that Roya Nobakht is another British-Iranian being held in Evin prison.
She was jailed for five years in 2013 for making anti-government comments on Facebook.
A Government spokesman said: "We are doing everything we can for the British-Iranians detained in Iran. These cases have been raised at the highest levels, including by the Prime Minister and Foreign Secretary, and we continue to work relentlessly to secure access to them and to make sure their welfare is protected.
"Our approach is based on decades of experience of dealing with Iran, and helping detainees around the world, and we judge it to be in their best interests. We will continue to keep it under constant review.
"Iran does not recognise dual nationality, it considers these detainees to be solely Iranian, and as a consequence does not believe the UK should have any involvement in these cases."