Gordon Brown is on familiar territory. The former prime minister is parked on a sofa in a family centre in the heart of his old constituency and holding forth about poverty.

The venue, a family centre called the Cottage, is in the Templehall part of Kirkcaldy and easy to miss. The poverty that it is helping to alleviate is not. When it launched its first Christmas appeal eight years ago – the year Brown’s Labour government was turfed out of office – the centre assisted 80 families. Last year it was 950: this year it will be 1,200.

Were it not for Brexit, Labour would be pushing poverty to the top of the political agenda. Jeremy Corbyn used all his allotted interventions at prime minister’s question time last week to quiz Theresa May about poverty and Brown has been giving the man who followed him as Labour leader his support.

Food banks have become a feature of modern Britain but Kirkcaldy has estates that are the most deprived in Scotland outside of Glasgow. Some families need more than food: they lack cookers and enough money to feed the gas meter.

Marilyn Livingstone, the family centre’s chair, says people are referred to the charity by churches, schools and social services. “The Cottage is a lifeline; it used to be the welfare state. It’s the not-so-poor helping the poor.”

Local people are generous. While Brown is visiting, two nurses turn up with two big sacks of newly bought Christmas presents acquired with money that staff at the local hospital would have spent on Christmas cards and secret Santas. The nurses are more typical than the thieves who broke into the centre and stole £800 raised to provide Christmas dinner for vulnerable people. “We are a strong community,” Brown says. “Local people have come together.”

As chancellor between 1997 and 2007, Brown used the tax and benefit system to tackle child poverty. He introduced tax credits to top up poverty pay and made child benefit more generous. The downward trend in child poverty that Labour bequeathed in 2010 has been reversed and is on course, Brown says, to hit 5 million by 2022.

Asked how that makes him feel, the former PM says: “It makes me angry. I’m seeing poverty I didn’t think I would ever see again in my lifetime. Slum housing was a feature of my childhood in the 1950s and 1960s, and I thought we had finally got over the worst of child poverty. Tax credits were the key to that.”

Brown has been especially critical of universal credit, which replaces six benefits with a single monthly payment. After widespread criticism, the current incumbent at the Treasury, Philip Hammond, announced an extra £1.7bn for UC in the budget and says the switch would happen more slowly.

Brown is unimpressed. “You can’t solve child poverty with the existing system,” he says. “Universal credit is completely underfunded and every time they move people on to it you see more poverty. Minimum wage jobs don’t pay enough to keep a family with two or three children out of poverty.”

Vicki Hutchison, a single mother with two daughters aged six and 10, says she finds the support provided by the Cottage invaluable but is clear that the move to UC has made her worse off.

Facebook Twitter Pinterest Volunteer Vicki Hutchison helps with The Cottage community centre Christmas appeal. Photograph: Murdo MacLeod/The Guardian

She says that when she was moved on to the new system there were no payments at all for six to seven weeks and she had to take out advances against future payments that meant that when the UC did kick in a chunk of it was held back to repay previous loans. “I was getting half what I was entitled to and it is not enough to pay all the bills, and to feed and clothe my kids.

“Every single person around here is one pay cheque from being where I am. I think of myself as a failure. My eldest understands. She says: ‘I know we can’t have that mum because we don’t have much money just now.’”

Hutchison, who went to college to get qualifications in catering and events management, says she cannot find a job that will pay enough to cover her childcare costs and adds that the need for outside help makes her feel like a failure. “You should be able to look after your kids.”

Child poverty in Britain was once concentrated among the unemployed. Today, a combination of low pay and a much less generous welfare system means that two-thirds of poor children are in working households.

“The government is trying to analyse this as people who are too lazy to get into work,” Brown says. “But the problem is that people can’t earn enough to stay out of poverty.”

Famed as the birthplace of the 18th-century economist Adam Smith, Kirkcaldy once had coal, textiles, linoleum and electronics. Today the biggest employers are the NHS and the council, and it faces the same economic problem as many other medium-sized UK towns: it is a bit too far away from the nearest big city – Edinburgh in Kirkcaldy’s case – for local people to travel to where there are better-paid jobs.

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The Cottage runs a dads’ project, a mental health project and a grandmother’s club to help grandparents who are the main carers for children. It tries to help parents ensure their babies grow up to be healthy.

Over the past three years, a period since George Osborne used his summer 2015 budget to cut welfare spending by £12bn a year, the caseload had increased dramatically, Livingstone says. She praises the council, which she says does a good job despite the cuts to local government budgets over the past eight years.

Like Brown, she does not buy the Government’s argument that the new benefit system will be simpler and provide better incentives for people to work. “Introducing universal credit was the straw that broke the camel’s back for a lot of people.”