A leaked staff memo at the Department for Work and Pensions (DWP) appears to show the government is still struggling to roll out its flagship welfare programme, universal credit (UC), across the UK.

The memo, seen by the Guardian and titled: “Ideas please: Sinking”, appears to be a plea from a jobcentre manager to her staff for solutions to tackle an ever-growing workload brought about by the new system for delivering social security to more than 7 million people.

The internal email, sent in late September and uncovered by Channel 4’s Dispatches as part of an investigation into UC to air on Monday evening, appears to show that one of the 60 centres where the scheme has been rolled out is generating such a substantial backlog of claims, centre staff will have to work three times more than their limit to clear it.

UC, which is projected to generate £7bn in economic growth to the UK, will combine six benefits, including jobseeker’s allowance and housing benefit, into a single payment, which will rise and fall more smoothly with people’s circumstances.

The DWP had promised to have 1 million people on the scheme by April 2014 but, dogged by delays and tens of millions of pounds of IT write-downs and write-offs, the original timetable has been scrapped. Just 15,000 people are on the system.

Last week, the work and pensions secretary, Iain Duncan Smith, declared that the project would not be tied to a final delivery date. “Arbitrary dates and deadlines are the enemy of secure delivery,” he said.

A jobcentre employee has alleged that the UC claims process, which is meant to save the government hundreds of millions in staff costs by being highly computerised, is unable to handle complicated cases. The whistleblower told Dispatches:“The IT works for single claimants, the straightforward cases. More complex claims have to be done manually. That’s slow and easy to get wrong.”

He added that UC’s IT for staff on the ground is “completely unworkable, badly designed”, and already “out of date”.

The DWP minister, Mark Harper, has denied any problems. He said he had spoken to frontline staff at the 100 service centres rolling out UC and received “nothing but positive feedback”.

A DWP spokesperson added: “There is no evidence that more complex cases cannot be dealt with successfully.”

The Guardian has previously reported on how leaked Whitehall documents warned of a failing IT system, more than £1m in wasted expenditure, and how only 25,000 claimants would likely to be served by the system by the the general election next year.

The government has written off or written down £130m on the project, which is designed to revolutionise the culture around claiming benefits. It now expects 100,000 people to be on the system by May and for 100 centres to be involved in its delivery by the end of this year.

The Dispatches investigation will also allege that UC’s failures are leaving claimants in desperate circumstances. One couple told the programme it took three months to register their change-in-life circumstances, leaving them struggling to feed themselves and their child.

Jay Montrose had previously been living on his own and claiming UC as a single person. In June he moved in with his partner, Nikki Colton, who is pregnant, and their four-year-old son, Ethan.

After being informed they would be treated as joint claimants under the scheme, Montrose and Colton told Dispatches their claim took so long to process, they were unable to pay for food, rent and other bills, built up debts of £2,500 and eventually received an eviction notice from their landlord. The couple said they received the correct money only after staff told them their claim was being processed manually.

“I was worried because I’m pregnant at the moment and I should be eating at least enough to get me through. I shouldn’t be living off a packet of crisps in the day because that was all that [we had] that could be spared and that Ethan didn’t need,” Colton told Dispatches.

The DWP said the couple’s claim had been delayed because the pair had failed to complete the correct forms. Responding to Dispatches’ findings, a spokesman told the Guardian: “Universal credit’s IT system is robust and effective, and we have trained 26,300 work coaches who are successfully providing new support to claimants to help them better prepare for work.

“We are rolling UC out in a safe and controlled way to ensure we can make changes to the system if necessary. But there is absolutely no evidence that cases cannot be dealt with. When fully rolled out, UC will make 3 million families better off by £177 a month and lift up to 300,000 children out of poverty.”

• Dispatches: Benefits Britain is on Channel 4 at 8pm GMT on Monday 27 October