Prisoners have made it on to the roof at a privately run jail in the West Midlands only recently criticised by inspectors for its poor safety levels – causing experts to repeat their calls for the management of the prison to be removed from private prisons company G4S.

Three male inmates are on the roof of HMP Oakwood, which is operated by G4S, near Wolverhampton, the management confirmed.

In a statement, a spokeswoman for the security firm said: “We can confirm that an incident involving three prisoners is taking place at HMP Oakwood.

“The Ministry of Justice has been alerted and our normal contingency plans have been enacted.”

The spokeswoman would not discuss how the prisoners had made it to the roof.

The incident comes after the publication on Tuesday of a surprise inspection by Her Majesty’s Inspectorate of Prisons (HMIP), carried out in June, which listed a host of safety and operational concerns including the fact “too many prisoners felt unsafe”, while describing prisoner-staff relations as inadequate.

In July, the Ministry of Justice (MoJ) mentioned Oakwood as one of only three in the country which it listed as being “of serious concern”.

Following the HMIP report, the Chief Inspector of Prisons Nick Hardwick said the modern facility, which can hold about 1,600 inmates, was staffed by officers and managers who “seemed keen to do the right thing” and praised the standard of accommodation and the facilities.

However, he said: “There is a lot to do before Oakwood is operating anywhere near effectively.”

He added the management at the jail “urgently needed a plan to retrieve the situation”.

Mr Hardwick stated “prisoner frustration needed to be addressed”, particularly over access to basics like cleaning materials.

He also said “work to build the competence and confidence of staff” was needed and the prison needed to “communicate more effectively with prisoners”.

Overall, the report concluded that of the four healthy prison markers; safety, respect, activity and resettlement, inspectors found measures at Oakwood to be either insufficient or poor.

Oakwood is a category C training jail for male prisoners sentenced to three months or more, and opened in April last year.

Staffordshire Police said it had not received any calls from the jail.

Mark Leech editor of Converse the national newspaper for prisoners in England and Wales, who called last week for Chris Grayling,  the Secretary of State for Justice, to exercise his powers and bring Oakwood prison under the control of the public sector, said: “I would repeat my call for Oakwood to be removed from the private sector, but this is an on-going incident and while staff at the prison try to regain control it’s not appropriate to comment – but Oakwood is clearly a prison in very deep trouble.”