Government ministers may insist that soaring demand for food banks may have nothing to do with welfare reform, but for Louise, a homeless, quietly distressed 31-year-old unemployed ex-care worker, the link is clear.

In May she lost her job, and in late June she was evicted from her flat. She says the council's new local welfare scheme told her she was not eligible for crisis help, and the local jobcentre, having "fast-tracked" her claim for unemployment benefit, explained that she would have to wait up to three weeks for the first payment.

Until then she is penniless. Louise says she sought a short-term cash advance from the jobcentre to tide her over until her first benefit cheque but was not offered one. Jobcentre officials, she says, instead referred her to the charity-run Pecan food bank in south London to collect a food parcel. "I feel helpless and marginalised," she said.

At Pecan, the claim made by the work and pensions minister Lord Freud last week that there was no evidence of a correlation between rising food bank use and welfare changes is regarded with incredulity.

Chris Price, Pecan's executive director, says food banks risk becoming a precarious charitable safety net for a welfare system that is failing to provide the support to which claimants are entitled, and that that a voluntary project originally designed to meet tiny gaps in state provision is being almost imperceptibly sucked into a mainstream welfare role.

Local jobcentres and welfare changes are the biggest drivers of food bank demand, says Price. Benefits delays and benefits penalties, called sanctions, which typically result in claimants' payments being stopped for six weeks, are driving up food bank demand to the point where Pecan is finding it hard to keep pace.

Although Freud insisted that the welfare system was designed to "support people with advances of benefit where they require it", Price says that in his experience jobcentres are instead referring vulnerable claimants to food banks. "They [jobcentre staff] do not use it [the cash advances system] or they are advised not to use it."

He adds: "The jobcentre official is saying to the claimants in effect: 'We cannot give you any money, but here's a voucher for a food bank because we don't want to see you starving.'

"If claimants are coming to us instead of getting a short-term advance then they are getting food, but if we keep doing that it puts us in a position where we are becoming part of the welfare state."

Pecan says the rapid growth in referrals from the local welfare system began a few months ago but has accelerated since April, when several welfare changes were introduced. Between 1 April and 31 May it fulfilled 486 vouchers, of which 117 came from three local jobcentres. Over the same period in 2012 none of the 134 vouchers fulfilled were from jobcentres.

Benefit changes – people being shifted from one benefit onto another – and benefit delays have accounted for 210 of those 486 vouchers, says Pecan. A further 33 food parcels were issued to people turned down for crisis help by the council's crisis welfare scheme, which was introduced in April when the social fund was abolished.

Even that does not tell the full story, says Felicia Bolshorin, a Pecan staff member. People arrive at the food bank having been formally referred by other agencies, such as Citizens Advice, but when they are interviewed it often turns out that their financial problems are caused by benefit delays or loss altogether.

Bolshorin says she wrote to the local jobcentres a fortnight ago pleading with them to stop referring so many claimants, because the food bank was finding it difficult to cope with the demand. "Two weeks ago I interviewed 29 clients and 17 of them were referred from Jobcentre Plus. I'd say 99% of them had been sanctioned."

Food banks like Pecan are dependant on the public donations for food, and Price says he is worried that the public will be more reluctant to give if they feel the food bank is being used as a substitute for social security entitlements.

In Bristol the founder of the Matthew Tree Project food bank, Mark Goodway, says it has purposefully refused to take referrals from Jobcentre Plus because it anticipated that it would not be able to cope with the number of referrals. But despite this, jobcentres gave out maps to claimants instructing them how to get to the food bank anyway.

Clients referred to the food bank by other agencies often have problems rooted in benefit delays or sanctions, says Goodway. "I saw a client [recently]. The good news was that his claim had been accepted. The bad news was that he was going to have to wait six to eight weeks for his money to come through.

"He will be destitute for up to eight weeks, and that's happening across the board. What are these people supposed to live on?"