Fire and ambulance workers were also at the scene, Reuters reports.
"There's been a serious incident which has resulted in two wings being taken over by prisoners," a spokesman from the POA union, which represents prison officers, told Reuters.
"Prison officers from all over the country are being bussed into Bedford now.
They will take over the situation and deal with it as a riot and bring the establishment back under control," he said.
The local ambulance service said units remained on standby, with no casualties reported.
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