The cost of the government’s flagship welfare programme could rise by billions of pounds if it fails to meet a challenging timetable to introduce a new IT system, Whitehall’s public spending watchdog has found.

A digital service to handle universal credit (UC) claims for 7m households has not yet been tested on anyone and has already been delayed by six months this year, the National Audit Office disclosed. If there is a glitch and the government is forced to rely on old technology, auditors believe it could cost taxpayers an extra £2.8bn in staff costs.

The report, issued on Wednesday, completes a miserable 24 hours for the welfare secretary, Iain Duncan Smith, who was forced to admit to parliament that the scheme, which was supposed to be fully implemented by 2017, will not be ready before the end of the decade.

Ministers have privately expressed dismay at the way Duncan Smith has handled the rollout. He has repeatedly told parliament and Conservative activists that it is “on time and within budget” as the completion date has been pushed back. Margaret Hodge, the chair of the public accounts committee, said the scheme was in a precarious position and the Department for Work and Pensions was “throwing good money after bad”.

“The digital service is already delayed by six months and the department has just 18 months to get it up and running as planned,” she said. “The department’s unacceptably poor management of this programme has wasted time and taxpayers’ money, with a staggering £600m spent in four years just to get to the first stage of business case sign-off.”

Duncan Smith set out to transform the benefits system in 2010 by launching universal credit as a £2.4bn scheme to merge six benefits into one. The entire scheme was “reset” in early 2013 with £34m written off on the failed IT programme and the original deadline was put back two years.

He also introduced a “twin-track” system, which meant that a new online digital service has been developed while a “live” IT system has been in operation since 2013. The live systems have been implemented in 80 job centres so far.

If the new digital service is not established, the report estimates that using live systems without further investment could cost £2.8bn more in staff costs alone.

Auditors have also concluded that running two systems is costing £300m more than rolling out the programme at a slower pace. They say it is too early to tell if the plans will be value for money.

A table in the report shows the government’s ambitious 18-month programme to roll out its full digital service. Officials hope to test between 100 and 500 claimants this month; up to 5,000 by next summer whilst integrating five other systems; and up to 10,000 using 20 automated links to other systems; rising to 10 million claimants by May 2016. Ministers have also failed to put contingency plans in place to cope with setbacks in the digital service, the report said. So far, 17,850 claimants have received a UC payment.

Rachel Reeves, the shadow work and pensions secretary, said the NAO had cast grave doubts over the future of universal credit. “The National Audit Office report is further evidence that the government’s handling of universal credit has been disastrous. It’s neither on time or on budget as the government promised,” she said.

A DWP spokeswoman said the “twin-track” approach would result in net savings for the government and that the investment costs for UC had been reassessed as being £1.8bn. “The NAO report recognises that we are reducing risks and making progress. In terms of value for money, when fully in place the economy will benefit by £7bn each year and is set to make 3 million families better off on average by £177 a month,” she said.