Lord Carey, the former Archbishop of Canterbury, has called on leading British Muslims to support the right to convert from Islam to another religion after a court in Sudan sentenced a woman to death for apostasy.

The peer said it was “accepted doctrine” that Muslim converts should face the death penalty. He also said there were examples of ex-Muslims in Britain who had been forced to “almost go underground”.

“Isn’t there something fundamentally wrong with Islam at its core that it cannot allow people to change their religion?” he told The Sunday Times.

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“It is accepted doctrine in Islam [that] you don’t convert and if you do the penalty may be death.” He added: “I want to hear Muslim leaders say ‘we allow Muslims to become Christians if they wish to’.”

Lord Carey spoke out after Meriam Ibrahim, 27, was sentenced to death by a sharia court in Sudan after refusing to recant her Christian faith. The sentence has been suspended as she is pregnant.

But a leading British Muslim thinker Dr Ghayasuddin Siddiqui told The Independent that the Koran said people should have the freedom of religion.

The idea that former Muslims should be put to death was introduced later as part of “man-made sharia” law, he said, adding that the issue was being debated by Muslim scholars around the world.

“I think hopefully at some stage consensus will emerge that this is a very divisive, anti-pluralism approach and it must be abandoned,” he said. “The basic rule of the Koran is there is freedom [of religion]… the basic rule of Islam is there’s no compulsion in religion.”

Asked whether Muslims should be allowed to convert, Dr Siddiqui, a fellow of the Muslim Institute, said they “should be allowed to do whatever they want”.