Calls are growing for the release of three British citizens imprisoned in Iran amid fears that at least two of them may die behind bars.

After Iran freed four dual US-Iranian nations following the lifting of international sanctions against the Islamic republic, some MPs as well as Amnesty International say the UK government should be pushing Tehran for the release of the British citizens held at the notorious Evin prison near Tehran, which has a special wing for political prisoners.

They include Roya Nobakht, 49, a woman who made anti-government comments on Facebook and the 76-year-old businessman Kamal Foroughi, who was jailed in 2011 for eight years for espionage. The identity of the third British citizen has not been released.

Foroughi's family, who believe his only crime was regularly travelling to the UK and having British friends, say he did not receive a fair trial.

His son Kamran told The Independent he was worried that his increasingly frail father might "die a lonely old man in prison".

Campaigners say Roya Nobakht has been subjected to "physical and psychological torture" in jail and recently collapsed in her cell after being denied access to medication for depression.

Amnesty's individuals at risk campaigner Kathy Voss also told the newspaper: "With UK ministers hailing the nuclear deal, you have to ask – where is the pay-off for the British detainees still behind bars in Iran?"

Hilary Benn, the shadow Foreign Secretary, said the Government should be doing all it can to get them released while other MPs said they hoped better ties between Tehran and London could help speed their release.

A Downing Street spokesperson said David Cameron had discussed the British cases with Mr Rouhani in a telephone call on 19 January.

"The Prime Minister raised concerns over three dual UK-Iran nationals held in Iranian prisons, pressing for swift progress in their cases. Acknowledging this was a humanitarian issue, President Rouhani undertook to look carefully at the cases," the spokesperson told the Independent.

The Washington Post journalist Jason Rezaian, was among the Iranian-Americans released in January.