The vast majority of companies set up to tackle reoffending as part of a controversial drive to privatise the probation service have failed to meet their targets, in a substantial embarrassment for the government.

Dramatic official figures have revealed that only two of the 21 regional companies set up to oversee low and medium-risk offenders have managed to reduce the number of new offences committed by reoffenders.

The revelation comes amid claims that the probation system is in crisis. Senior figures in the service warn that the companies involved lack the resources to do the job, while staff shortages have already meant that some ex-offenders are supervised by telephone calls.

The failure emerges just weeks after the public spending watchdog, the National Audit Office, warned that the new “payment by results” system meant that a failure to hit reoffending targets could blow a further hole in the service’s finances. The companies involved have already required an extra £340m.

It is another sign of the difficulties facing public services after years of public spending cuts. Theresa May is already under pressure over NHS funding, with a crisis also hitting the nation’s prisons system. The supervision of offenders not deemed high-risk was handed to 21 community rehabilitation companies (CRCs) in 2014, as part of a privatisation drive by the former justice secretary Chris Grayling. Companies were to be partly paid in relation to their success in reducing reoffending.

However, official figures from the first year of the new system’s operation reveal that, among the prisoners who went on to reoffend, the average number of crimes committed in 2015-16 went up in all but two areas compared with 2011.

It means that only the companies operating in Merseyside and Northumbria met their targets and are in line to receive a full payout from the Ministry of Justice. The remaining 19 could have a portion of their income cut as a result of the “payment by results” system.

These results follow a devastating official report at the end of last year in which Dame Glenys Stacey, the chief inspector of probation, said there was “no clear evidence that payment by results linked to reoffending rates [had] made any difference to the life chances of these or others under probation supervision.

“In those cases we inspected, only a handful of individuals had received any real help with housing, jobs or an addiction, let alone managing debt or getting back into education or training,” she said. “What is more, about one in 10 people were released without a roof over their heads.

“CRCs are too often doing little more than signposting and form-filling. Apart from Wales and Durham CRCs, we find that CRCs we have inspected are making little material difference to the prospects of individuals upon release, and yet this work is so important in breaking the cycle of offending.”

Andrew Neilson, director of campaigns at the Howard League for Penal Reform, said the data revealed significant flaws in the privatised service. “The rhetoric at the time of the privatisation was all about payment by results and improving the fight against reoffending,” he said. “But that was really just a smokescreen for something that was about cutting costs and taking money out of the system.

“When you put these figures alongside Glenys Stacey’s report, it is impossible to avoid the conclusion that this was about taking money out. When you boil it down, this is a service where companies are failing and being paid to fail because of a botched privatisation.”

The Ministry of Justice said that there were now fewer offenders overall and that those who remained in the criminal justice system were more prolific offenders – which explained why the numbers of new offences per reoffender were increasing.

“Our probation reforms mean we are monitoring 40,000 offenders who would previously have been released with no supervision,” a spokesperson said. “Overall, community rehabilitation companies have reduced the number of people reoffending, but they need to do more to ensure we have a service that keeps the public safe and helps offenders turn their back on crime.

“Probation officers are doing an incredibly professional job, and we will continue to work closely with CRCs to improve performance.”

The department also said that those companies that had failed to meet targets would face deductions in their fees.