Daniel Wani says he hopes international outcry will lead to conviction of his wife Meriam Ibrahim being overturned

The prime minister and other political leaders have added their voices to the campaign to lift the death sentence given to Meriam Ibrahim, a Sudanese woman sentenced to hang for apostasy.

David Cameron's announcement came after Ibrahim's husband, Daniel Wani, appealed for global support to free his wife from death row, where she is being held with her two young children after giving birth in shackles this week.

Cameron said he was "absolutely appalled" when he heard of the decision.

"The way she is being treated is barbaric and has no place in today's world. Religious freedom is an absolute, fundamental human right," he said. His words were echoed by Ed Miliband, Nick Clegg and Tony Blair. Blair said it was a "brutal and sickening distortion of faith".

Wani, a US citizen since 2005, said mounting international pressure could have a significant impact on the Sudanese authorities, and he felt overwhelmed by "the way people have come together around the world" to protest against his wife's sentence. "I want to thank everyone for this stand. It's looking like it had an effect. Perhaps it will result in the judgment being overturned," he told CNN.

Ibrahim was sentenced to 100 lashes for adultery and to death for apostasy this month. She told a court in Khartoum that she had been brought up as a Christian, and refused to renounce her faith. She and Wani married in 2011, but the court ruled that the union was invalid and that Ibrahim was guilty of adultery.

Ibrahim, a graduate of Sudan University's school of medicine, has been told that her death sentence will be deferred for two years to allow her to nurse her baby.

Condemnation of Ibrahim's death sentence has gathered momentum. Hundreds of thousands of people have signed an Amnesty International petition in support of her release, including more than 150,000 in the UK. More than 600,000 people have added their name to a separate petition on change.org.

Justine Greening, the international development minister, tweeted: "Sudan must not allow the execution of Meriam Ibrahim to go ahead. #SaveMeriam." Mia Farrow urged her Twitter followers to bombard the Sudanese embassies in London and Washington with calls demanding Ibrahim's release.

Ed Miliband said the situation was "utterly appalling" and an abhorrent abuse of Ibrahim's human rights.

"Nobody should be persecuted because of the religion they practice or the person they fall in love with," he said.

"I cannot imagine the suffering - both physical and emotional - that Meriam, her husband and their two young children must be going through.

"The Labour Party has already asked British ministers to apply pressure to the Sudanese government to ensure her release. The British government will have our full support in their attempts to resolve this matter.

"Regrettably, this is one of many examples across the world of Christians being persecuted for their faith. The international community must come together to end this worrying trend."

The archbishop of Canterbury, Justin Welby, backed a statement from the Christian Muslim Forum in Britain calling for the sentence to be rescinded. "I wholeheartedly endorse this call … for the death sentence against Mariam Yahya to be dropped," he said.

Ibrahim, 27, gave birth to a girl in a prison clinic this week while shackled by her feet to the floor. Guards needed permission from the prison director to remove the chains, which was not obtained, her lawyer, Elshareef Mohammed, told the Guardian.

Wani was allowed to visit his wife, their new baby Maya and their 20-month-old son Martin on Thursday at the Omdurman women's prison near Khartoum. "She is a beautiful baby, and they are all fine," Mohammed said. "Martin is with her, and is a bit jealous of the baby."

He added that Ibrahim and her children were being kept in the prison clinic, and Wani had been given permission to visit her twice a week. The shackles were removed on Wednesday.

Siha, a coalition of women's rights organisations in the Horn of Africa, said it had been informed that Ibrahim had given birth in atrocious conditions and had been denied adequate medical care. It described her situation as dire.

Both Wani and Mohammed said the US authorities in Khartoum had failed to press for Ibrahim's release. "It's not the US government. When the problem began, the US consul here had a very negative position on this. She was very high-handed. She said, and I quote: 'I don't have time,'" Wani told CNN.

"The US embassy is not giving help," Mohammed said. No one was available for comment at the embassy in Khartoum .

The state department spokeswoman, Jen Psaki, said on Thursday that US officials in Khartoum had conveyed grave concerns about the case to the Sudanese foreign minister this week, and were closely monitoring the appeals process.

"We're doing everything we can to push for her release," she said.

The couple's lawyers have lodged an appeal against Ibrahim's convictions. "We don't know when there will be an outcome," Mohammed said.

Wani said his wife was committed to her Christian faith. "Even last week, they brought in sheikhs and she told them: 'I'm pretty sure I'm not going to change my mind.'"

Wani, who has muscular dystrophy and uses a wheelchair, lives in Manchester, New Hampshire. After he married Ibrahim, he took steps to bring her to the US.

The Foreign Office has described the sentence as barbaric, and summoned the Sudanese charge d'affaires to hear its "deep concern". The UN, Canada and the Netherlands have also called on the Sudanese authorities to overturn the convictions and release Ibrahim.