Vulnerable people are struggling to access food vouchers and cash grants introduced under a government scheme to help with the cost of living crisis.

The £1bn household support fund (HSF) has been beset by problems, with councils stuck trying to figure out workable payment methods to help those in acute need of financial support.

Ministers launched the HSF last autumn, initially pledging £500m and instructing local councils to distribute the money among poorer households in order to help with food, clothing and utility costs. The fund was later doubled in May and extended until the end of September.

David, 31, a social worker from Liverpool, is one of a number of people who told the Guardian Community of their experience of applying for the small government cash grants.

In February, David received a £60 grant from his council for gas and electricity in the form of a paper voucher and the instruction to redeem it at a shop with a PayPoint.

“I was unable to cash this in, despite visiting over 10 local PayPoint registered shops, all independent corner shops,” he said. “I was told to come back later, that the manager needed to authorise it, that the ‘system’ was down, I got a wide variety of excuses.

“In the end I threw the voucher away. It was incredibly frustrating.”

Nicola, who lives in the borough of Westminster and is on universal credit due to chronic illness, successfully accessed two HSF grants herself worth £150 each, and has helped various other people from her local constituency of Westminster north navigate what appears to be a Kafkaesque application and redemption process she described as “a nightmare”.

“The government has come up with this convoluted, chaotic system by giving the money to local authorities, which eat into the fund, then individually disseminate the money in different ways as they see fit. It’s a total postcode lottery,” she said.

“In Westminster borough, you have to apply to the Citizens Advice Bureau for household support fund vouchers. During the first cycle, the application process was cumbersome, but you could self-refer and even apply without a national insurance number. By the second round, it had got completely bogged down in administrative hurdles. Now, there isn’t even a form to fill in, you have to phone Citizens Advice or be referred by a food bank or charity.”

Nicola spent hours on the phone calling advice hotlines to apply for cash vouchers she and people from about 20 households she was assisting were entitled to. “You have to jump through so many hoops and you’re exhausting yourself to get these tiny payments because you’re desperate. It took eight or nine weeks to get the vouchers,” she said.

But problems did not stop there. “Westminster borough only issues Sainsbury’s vouchers, which do not help with electricity or gas bills, and you can’t buy infant formula,” she said.

She added: “Then there were lots of cases where Sainsbury’s staff didn’t recognise the vouchers people brought into stores, and some people just don’t have the social capital to argue their case.

“These many layers of bureaucracy – it’s ideological, to make it harder for people.”

A spokesperson for Sainsbury’s said the company was not aware of any customer complaints or issues with its gift cards being redeemed in store.

PayPoint said its network disburses up to 210,000 emergency fund vouchers at a value of £16m a week, and claimed that 97% of participating retailers have successfully processed a redemption payment. The company was however unable to share the overall redemption rate of cash vouchers across its network, saying this was sensitive client information.

“When a council launches a new cash out scheme, all retailers within the area receive an email containing samples of the vouchers and a text message alerting them to an anticipated increase in customers,” the company said, adding that it provides retailers with cash floats and cash safes upon request.

In the “occasional instance” where a retailer refuses to process a payout, the company said, typically due to a lack of funds in store, consumers could visit another PayPoint location at “minimal inconvenience”.

A spokesperson for the Department for Work and Pensions declined to comment on household support fund vouchers, and referred to local authorities “who are responsible for the distribution of the HSF in their local area”.

Cllr David Boothroyd, Westminster city council’s cabinet member for finance and council reform, said nearly 2,000 local households had been helped with these vouchers since the scheme launched.

“As with any scheme where there has been overwhelming demand, a small number of problems were raised. In most cases these were resolved, and we are working closely with CAB to extend their service,” he added.

“We are not aware of any complaints about Sainsbury’s staff but would be happy to investigate.”