Persecution of Christians in Iran is as bad as it was three years ago, in spite of the pre-election promises of the president, according to a new report.

Christians continue to be arbitrarily arrested and interrogated because of their faith. Some face "severe physical and psychological torture" during detention, and simple prayer or Bible study meetings are regarded as political activities that threaten the national security of Iran, the report says.

Churches can be closed down if they use the national language, Farsi, and Christians are regularly given long prison sentences and beatings. The worst punishments are reserved for those who convert to Christianity from Islam, when they are caught gathering in their informal house churches, and for their pastors.

Two all-party parliamentary groups, Christians in Parliament and International Freedom of Religion or Belief, joined forces to investigate the persecution of Christians in Iran.

The report details the case of one man sentenced to death simply for questioning some of the tenets of Islam on social media. Sadeq Saba, editor of BBC Persian, told the inquiry: "I hear from some people that the reason the regime is taking such a tough line against people like him is because a lot of people are becoming disappointed with Islam as a religion because of what the regime is doing."

Many cases are kept secret, but more than 90 Christians were known to be behind bars in Iran at the end of 2014. Raids and arrests in Christian homes are common, and recently a 12-year-old boy was physically abused during such a raid.

One woman told the inquiry by video link of how she asked three men who raided her house what they had done to deserve the treatment: "Are we murderers? Thieves? Criminals? The man swore at me. He said it would be better for me to be a murderer or a thief than a Christian or a Jew."

Christians disappear for weeks at a time while they are interrogated. They are held in solitary and questioned nightly, for hours at a time, beginning just after midnight. A key goal of the security services is to find and remove any New Testaments from the homes of Christians. Detainees are sometimes told they must to convert to Islam or their families will be killed.

Mohammed Zamir, a church leader in the UK for expat Iranians, said at the launch of the report at the House of Commons yesterday that hundreds of thousands of Iranians were converting to Christianity and it was out of control of the authorities. "They are responding to evangelism and they are responding to the message and they are converting to Christianity, literally in masses."

He said he witnessed a recent baptism of a woman who two years ago had been a devout Muslim. She had begun to question Islam after watching an item on the news about the arrest of dozens of Christians, the confiscation of their Bibles and closure of their churches. She was intrigued to know what it was about Christianity that made the authorities "so frightened". Her search for the answer to this led to her conversion.

The conservative MP David Burrowes and Baroness Berridge, co-chairs of the inquiry, say in a joint letter in the report that they had hoped the election of Hassan Rouhani in August 2013 would soften the regime's harsh treatment of religious and ethnic minorities. Sufis and Baha'is also suffer severe persecution.

"Sadly, we have been disappointed that his positive promises and moderate language have not translated into any meaningful improvement. The persecution remains as severe today as it was in 2012." That was when Christians in Parliament produced their first report on the issue.

They are calling on the Government to put pressure on the Islamic Republic to improve the plight of Christians and other minorities.