A review by prison inspectors followed a damning inspection of Liverpool's HMP Altcourse last year.
The Ministry of Justice disputes the figure, saying its own review puts the number of un-monitored individuals at 5,450.
It highlights concerns about HMP Woodhill in Milton Keynes, but says the governor is taking action.
Inspectors say reducing psychoactive drug use is key to HMP Stoke Heath flourishing.
The high security prison is well led and making progress, but is told to improve safety and conditions.
A report by the prison inspectorate highlights problems including overcrowding at HMP Winchester.
A new inspection of HMP Bullingdon finds drug availability is leading to increased violence.
Inspectors say the cause of John Keenan's death was not known when they reported on Haverigg Prison.
Inspectors praise staff for improvements since 2022, but safety concerns remain.
