Another two jails will be closed, saving £11.4m a year for Kenneth Clarke's justice department, which faces a 23% cut

Two prisons will be closed and nine more put out to competition in a mass privatisation programme, the justice secretary, Kenneth Clarke, has announced.

The prison closures include the much-praised resettlement jail, Latchmere House, in Richmond, west London, and Brockhill prison near Redditch, a 1960s prison building now in a poor state, which first opened as a remand centre and has at different times been both a women's and a men's prison.

Their closure will save £4.9m this year and produce an ongoing saving of £11.4m a year for Clarke's justice department, which faces a 23% budget cut.

The decision to put nine prisons up for competition – including the Wolds, which is already run by the private security company G4S – is potentially the largest single privatisation programme in the history of the prison service in England and Wales.

It is possible that some jails may remain in the public sector after bids are invited later this autumn. The last round of competition in March saw four prisons put up for tender and one, Buckley Hall, stayed in the public sector. The largest, Birmingham prison, is to be taken over by G4S.

The muted response to that decision by the Prison Officers' Association is likely to have been a factor in Wednesday's announcement that a further nine jails are to be market-tested.

The list includes HMP Lindholme, HMP Moorland and HMP Hatfield, all in Doncaster; HMP Wolds in East Yorkshire, which was the first private prison in Britain; HMP Acklington and HMP Castington, both near Morpeth in Northumberland; HMP Durham; HMP Onley near Rugby; and HMP Coldingley near Bisley, Surrey, which is a purpose-built training prison.

Already 12 of the existing 138 jails are run by the private sector. A further four new prisons are already earmarked to be built and run by the private sector.

If the private security sector succeeds in taking over eight of the nine prisons now being put for tender – and that is not a foregone conclusion – they will have 15% of the prisons "market" in England and Wales. Private security companies have long campaigned to create a viable private prison sector in England and Wales and this competition round could prove the tipping point they have craved.

The justice ministry says decisions about which prisons were selected for competition or closure were based on a wide range of criteria, including potential for improvement and innovation, and not just on the basis of the poorest performers.

The closure of Latchmere House and Brockhill will mean a reduction of 377 places in prison capacity in England and Wales. The capacity is to be replaced by new jails providing 2,500 extra places this year. Two other small prisons, Lancaster Castle and Ashwell, were closed earlier this year.

Latchmere House has a long history, which includes a period when it was called Camp 020 and was MI5's secret wartime interrogation centre where German agents were "broken" and some turned into double agents. More than 500 spies are thought to have passed through Latchmere House during the war.

Clarke said: "The public have a right to expect continuing improvement in the quality and efficiency of public services, without compromising public safety. The competition strategy and adjustments to the prison estate will help ensure that this is the case."