Ministers transferred back-office functions – human resources, payroll and accounts – to the private sector two-and-a-half years ago in a plan which was supposed to “radically improve efficiency across departments”.

At the time, the cabinet minister Francis Maude said: “There is absolutely no need for departments and arm’s-length bodies to have their own back-office functions, and duplicate efforts, when they can be delivered more efficiently by sharing services and expertise. Plus it will save the taxpayer half a billion pounds a year.”

The National Audit Office has examined the “shared services” initiative and found that instead of saving at least £128m a year, it has saved £90m – £4m less than it has cost.

In a highly critical report, auditors said that delays in its roll-out mean that costs will continue to rise.

Confidence in the entire project “is now low”, the NAO found, with further costs also incurred in drawing up contingency measures and dealing with the fact delays have already rendered some elements of the new system out of date.

Auditors said the Cabinet Office “did not act in a timely and effective manner” because it “did not see this as its role” and had “only recently taken a more active approach to dealing with the issues that have been raised”.

Tom Watson, Labour’s deputy leader, said: “It’s shocking the Cabinet Office has failed to convince other government departments to adopt a programme that was supposed to deliver significant savings for the taxpayer.

“This comes after repeated warning from the NAO and the public accounts committee that the programme was not working. It’s yet another failure from the prime minister’s own department.”

Public and Commercial Services union general secretary Mark Serwotka said: “This is an all-too-familiar story of Tory ministers cutting and privatising, only to find they have wasted money and damaged services.

“We opposed the privatisation of shared services because we did not believe it would deliver the savings that were promised and we have been proved right.”

The 2013 civil service reform plan introduced by Maude saw the creation of two shared services centres which would handle human resources, payroll and accounts for up to 14 departments and their arm’s-length bodies.

The Cabinet Office signed contracts with two private sector companies – Arvato UK and Steria – to operate the centres.

Auditors found there were initial weaknesses in the programme and these were exacerbated by the Cabinet Office’s failure to take control of the project.

While recent governance and leadership changes had been welcomed by departments and the two private suppliers involved, the NAO warned that “previous efforts in this area have not produced results”.

It said: “The government has repeatedly failed to learn the lessons from its experiences of shared services.” However, it acknowledged that blame lay also with contractors Steria and Arvato UK.

The scale of the problems was underlined when an arm of the Department for Business Innovation and Skills pulled out of its contract arguing it was “no longer viable”.

The Cabinet Office has redrawn its projections and is now hoping for major savings. A departmental spokesman said: “As the report states, the Independent Shared Service Centres have already saved £90m, and are forecast to make a further £504m in savings for the government and police by 2023/24.