The Prison Officers Association blasted a "flawed and selective" report today calling for further prison privatisation.
The report by right-wing think tank Reform claims that private firms are better at running prisons than the public sector and all jails should be subject to open competition.
Two contracts to run five prisons - Acklington and Castington, which have since formed Northumberland prison, and three in South Yorkshire - will proceed to the next stage of the competition with an announcement expected next spring.
Mr Grayling said private firms will be brought in to all public prisons to run maintenance, resettlement and catering to save up to £450 million over six years.
But Reform, which receives funding from security firm G4S and others, said the government would be wrong to limit the role of private companies within prisons to small contracts such as maintenance and catering.
Some 10 out of 12 privately managed prisons have lower reoffending rates among offenders serving 12 months or more than comparable public sector prisons, Reform claimed.
Controversially, the think tank also called for an end to national pay bargaining for prison officers with pay and conditions to be set locally by governors.
POA general secretary Steve Gillan said: "This is a flawed and selective report with cheap headlines from an organisation claiming to be independent.
"Reform is a right-wing think tank which receives annual donations and sponsorship from the same private companies which currently operate prisons and services within the criminal justice system."
Prison Reform Trust director Juliet Lyon also queried the report, saying it masked "decidedly mixed results" as some private jails have proved effective but others have been criticised.
"It is almost impossible to compare the performance and reoffending rates of one establishment with another, partly because prisons hold different categories of offenders and also because prisoners often serve their sentences in a number of different jails," she said.
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