Prison governors have been ordered to cut the cost of holding inmates in England's bulging jails by £149m a year, as part of a radical programme designed to slash the costs of incarceration by £2,200 a year per prison place.

Detailed plans have been outlined by Michael Spurr, the chief executive of the National Offender Management Service (Noms), which would mean £900m, or 24%, will have been cut from prison budgets by next April since the coalition came to power in 2010.

However, despite pressure on already stretched budgets, Chris Grayling, the justice secretary, aims to go further and emulate the low-cost model adopted by the troubled, supersized G4S-run Oakwood prison near Wolverhampton.

The cost of running the 1,600-inmate Oakwood – a scene of significant disorder in January, which the authorities insisted fell short of a riot – is 31% less than the same type of public sector prison. It cost £15,500 a year per prisoner place to run when it opened in 2012/13 – compared with £22,000 for an equivalent publicly-run jail.

But a Guardian investigation published on Wednesday into the operation of Oakwood, based on speaking to several prisoners, paints a dispiriting picture of inexperienced staff struggling to keep control, with drugs rife.

One recently-released Oakwood inmate, Kev, said that staff were so inexperienced that "they were asking me what to do to keep order" and described the prison as "staffed by kids who should be stacking shelves".

A prison officer at the jail, speaking on condition of anonymity, spoke of a gap in knowledge between the relatively new staff and seasoned inmates.

Prisoners, experts and officials have also criticised the teaching and rehabilitation resources available at the prison. Experts say smaller prisons tend to have lower reoffending rates. The director of the Prison Reform Trust, Juliet Lyon, said: "Smaller prisons tend to be safer and more effective than larger establishments, holding people closer to home and with a higher ratio of staff to prisoners. Slashing prison budgets and introducing harsher regimes while warehousing ever greater numbers overseen by fewer and largely inexperienced staff is no way to transform rehabilitation."

Prison inspectors have separately criticised Oakwood as a jail where inmates say it is easier to get drugs than a bar of soap – a statement that is endorsed by former inmates, who say drugs packages are thrown over the fence.

But prison chiefs say that the new model jail is improving and expect it to have cut costs further this year to only £12,000 per prisoner place per year. This is 46% below the £22,420 cost of a prisoner in a similar publicly-run category C jail in England and Wales.

There are also concerns around self-harm. New figures from the Ministry of Justice have revealed that the number of incidents of self-harm are on the rise among the prison population in general. But two jails run by G4S, Oakwood and Altcourse, in Merseyside, are among the worst when it comes to self harm. There were 611 incidents of self-harm last year at Oakwood, near Wolverhampton, and 889 at Altcourse, which had the highest figure in England Wales. In contrast, there were only 81 and 56 self-harm incidents respectively in the London prisons Wormwood Scrubs and Wandsworth – publicly-run jails of similar size to Oakwood.

Under Spurr's plan the fresh savings are to be found by an extension of a controversial "benchmarking" programme under which the budgets of public sector prisons are to be driven down to match selected private sector jails. The benchmarking exercise is now to being extended to all high security jails, and will see staffing levels at comparable jails standardised and reduced and a new "core" day introduced to standardise the time spent by prisoners out of their cells.

Spurr said the savings can be achieved while maintaining good performance. "These savings are being achieved not by simply cutting services or reducing quality but by fundamentally reforming the way we work," says Spurr in his forward to the Noms business plan.

Whitehall auditors say the savings at the large jails have been achieved through economies of scale, and the increased use of closed-circuit television to enable lower staffing levels. But critics have attacked the government's increasing emphasis on privately-run "jumbo jails".

Reflecting the new thinking, building is due to start this summer on the first 2,000-capacity supersize prison outside Wrexham, which is due to open in 2017.

One key element of the cost savings drive has been the programme of closures, despite the near record 85,000 prison population and the increased volatility and disturbances that have been seen in recent months – some as a result of understaffing levels or inexperienced staff. Prison managers hope to have saved £423m by closing jails by 2015/16, and 15 jails with 7,000 places have been closed or are scheduled for closure or conversion to immigration removal centres.

They have been replaced by privately-run supersized jails with the 1,600 place Oakwood and the Serco-run Thameside prison in London, which currently holds 900 inmates but is due to expand to 1,200.

The extra 300 prisoner places at Thameside will to bring down the jail's cost from £50,000 per place to £22,000. Four new "houseblocks" are also to be provided later this year at Peterborough, Parc, and the Mount in addition to the extra 300 places at Thameside later this year to ensure prison chiefs do not run out of space.

New justice ministry figures contained in as yet unpublished Commons written answers to shadow justice secretary, Sadiq Khan, show where new cuts could come from: 246 more full-time prison officers were working across 63 prisons than the 9,234 officers determined to be needed in the first benchmarking exercise last December.

MPs on the Commons public accounts committee last week said that older prisons had been closed even when they were performing well, to be replaced by the two new large private prisons which had performed poorly since they opened.

Khan said: "The government's approach to running prisons is a cause for concern to many experts. Of course, we all want to reduce the cost of prison. The best way to do this is to ensure prisons are a place where offenders are reformed so they don't reoffend."

Justice minister Jeremy Wright said: "We have always been clear that we want a fit-for-purpose, modern prison estate that provides best value for the taxpayer and addresses our stubbornly high reoffending rates.

"We've had to make some tough decisions, including closing old inefficient prisons and introducing new ways of working, but it is a credit to the staff and strong leadership that we have continued to deliver safe and secure regimes while pushing ahead with our ambitious plans to transform the way offenders are rehabilitated.

"As the National Audit Office highlighted, our current strategy is the most coherent and comprehensive for many years."