The tax, called jizya, is being imposed by gangs of Islamist extremists at Belmarsh, Long Lartin, Woodhill and Whitemoor prisons, according to evidence supplied to the team.
All four prisons, which have a total capacity of 2,633 inmates, are rated category A, meaning they hold the most dangerous criminals, including terrorists.
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Some of the alleged victims said they were told to arrange for friends and family on the outside to transfer money to nominated accounts.
Faced with the option of paying up or suffering at the hands of the Islamists, some prisoners have been pressured into converting to Islam to ease their time in prison.
The claims will fuel fears that some Islamist inmates are operating inside prisons with impunity.
While jizya is sanctioned by the Quran, it has not been in use anywhere in the world since the mid-1800s until it was revived recently by Islamic State (ISIS) militant group, the report said.
A Whitehall government source told the newspaper: "(The imposition of jizya) shows the extent to which Islamist extremism in prisons is becoming a problem when you have inmates seeking inspiration from the likes of ISIS to intimidate and bully non-Muslims into paying for their safety."
"It sets a dangerous precedent and sends a message to non-Muslim inmates that Muslims are going to run the prison according to their own rules and sharia (Islamic law)," the source was quoted as saying by the paper.
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