Failings by the Ministry of Justice in the part-privatisation of probation services have been “extremely costly” for taxpayers, the National Audit Office (NAO) has said.

A review of Chris Grayling’s Transforming Rehabilitation programme, published on Friday, added that the number of people on short sentences recalled to jail had soared and the termination of contracts with private probation companies would cost at least £171m.

There has been a 2.5% reduction in the proportion of offenders proven to have committed another crime between 2011 and March 2017. However, the number of offences per reoffender has increased by 22%.

In 2013, the programme was launched by the Ministry of Justice (MoJ) under Grayling, who was then the justice secretary, with the aim of cutting reoffending rates in England and Wales and reducing costs.

It created 21 community rehabilitation companies (CRCs) to manage low- and medium-risk offenders, while the National Probation Service (NPS) continued to manage high-risk offenders across seven regions.

As a result of supervision by probation being extended to people serving less than 12-month sentences, the number of recalls to prison has increased by 47%.

Offenders on licence can be sent back to prison if they reoffend or break other probation conditions, such as missing meetings with probation officers without good reason or travelling abroad without permission.

Amyas Morse, the NAO chief, said: “The ministry set itself up to fail in how it approached probation reforms. Its rushed rollout created significant risks that it was unable to manage.

“Not only have these failings been extremely costly for taxpayers, but we have seen the number of people on short sentences recalled to prison skyrocket.”

Last July, the justice secretary, David Gauke, announced that private companies running CRCs would have their contracts terminated in 2020, two years earlier than agreed.

So far, they have received £467m in projected bailouts, a proportion of which was given to cover penalties owed by the companies for failing to meet targets under Grayling’s “payment by results” system.

When current contract-holders were in the bidding process, their collected forecasted profits were £269m, but by March 2018 CRCs faced collective losses of £294m.

Rory Stewart, the prisons and probation minister, said: “Transforming Rehabilitation has meant that we are now monitoring 40,000 more offenders than we were in the past. This is good for public safety.

“The performance of the CRCs is too often deeply disappointing. That is why we have stepped in to end contracts early and invested an extra £22m a year in services for offenders on release.”

Although the MoJ has set out a new strategy – which will reduce the number of aligned probation areas in England to 10 – the report noted it carried risks because offender management will still be split.

It also pointed out the risk of providers withdrawing services or failing outright in light of the collapse of Working Links, which owned three CRCs, last month. In the aftermath of the announcement, union bosses condemned Grayling’s “disastrous privatisation programme”.

Probation union Napo’s general secretary, Ian Lawrence, said: “Not only have the CRCs been unable to deliver services, the NPS also has significant failings.

“Staff shortages have resulted in unmanageable workloads across the board,” he added.

“A [Transforming Rehabilitation] mark 2 will not resolve the issue of the first reform programme and will only perpetuate the ongoing risks and issues we have seen over the last four years.”

Between January 2015 and September 2018, offenders on short sentences as a percentage of everyone who was recalled to prison rose from 3% to 36%.

Though the NPS performed better than CRCs, the NAO added that it had been constrained by severe staff shortages and high workloads.

A probation officer, who wished to remain anonymous to protect his identity from his employer, said he believed the NAO’s comments were “an understatement”.

He said: “There are staff shortages everywhere and poor retention of new staff due to rock-bottom morale.”

The NAO has called for the MoJ to publish a cross-government strategy to explain how it will work with other bodies to reduce reoffending and develop a plan to manage the winding-up of existing contracts.