UK justice secretary Liz Truss spoke on the issue after it had emerged over the weekend that specialist units were part of a wider review of the country's prison system to tackle extremism.
"Preventing the most dangerous extremists from radicalising other prisoners is essential to the safe running of our prisons and fundamental to public protection," Truss said.
"Islamist extremism is a danger to society and a threat to public safety - it must be defeated wherever it is found. I am committed to confronting and countering the spread of this poisonous ideology behind bars," she added.
The move comes soon after the conviction of one of the UK's most extremist preachers Anjem Choudary.
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He is expected to be jailed for 10 years after being found guilty of pledging allegiance to Islamic State (ISIS) at a sentencing hearing scheduled for September.
The review, which remains classified with only excerpts released to the media, looked at the risks posed by Islamist extremists in prisons, and also recommended prison officers, on the front line, be equipped to crack down on extremist behaviour.
Governors have also been instructed to ban extremist literature and to remove anyone from Friday prayers who is promoting anti-British beliefs or other dangerous views.
Lack of confidence in challenging unacceptable extremist behaviour and views was highlighted as a key concern across the prison estate, resulting in reluctance to confront extremist views.
Prison chaplains will also face more stringent vetting procedures to ensure that they are not linked to any extremist organisations.
Figures show there were 12,633 Muslims in prison in England and Wales as of the end of June.
Acheson said his report had concluded that the National Offender Management Service, which is responsible for correctional services in England and Wales, was "very far from being effective in both understanding and reacting properly to the obvious threat posed" by Islamist extremism.
"This must change in order to protect staff, prisoners and wider society and we have made dozens of recommendations to that end," he said in an email to the BBC.
His review found there was evidence of a weak understanding of Islamist extremists, including a lack of data on conversions and lack of management control over extremist literature and materials.