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£2.3billion Jobseekers Allowance. £2.86billion pension credit. £3.62billion in housing benefit. £2.83billion Income Support and Employment and Support Allowance.

As the welfare debate is spun by this government, these are the figures you will rarely hear.

These are the estimated amounts unclaimed last year by people who are perfectly entitled to claim benefits – including disabled and unemployed people, carers and pensioners.

According to figures quietly released last month by the Department for Work and Pensions, the total amount unclaimed is likely to be between £11.6bn and £13.23bn a year.

This adds up to tens of millions of pounds unclaimed every single day on ‘Benefit Street’. And it is around ten times the amount lost to benefit fraud – estimated by HMRC to be about £1.2bn a year.

Among older people, the shock figures include over 1.34 million people who fail to claim pension benefit – nearly two out of five who qualify.

The blogger and housing consultant Joe Halewood points out the amount unclaimed increases by billions when other welfare benefits – like tax credits – are included.

“In June 2011 HMRC published a report stating that £8.344bn per year in Tax Credits goes unclaimed,”

he says. “If that figure remains the same, it pushes the unclaimed total even higher.”

The total would be over £20bn a year. That’s more than £50m per day. And the sum doesn’t even include Council

Tax benefit as it is administered by local councils.

This week I spoke to the children’s centre project in Leeds behind a stunning initiative that has identified £1.2m in unclaimed benefits for local families.

“It is testament to the hard work of our advisers and telephone assessors that they were able to identify £1,202,680 of unclaimed benefits,” said Richard Bridge of Better Leeds Communities.

“It’s not difficult to imagine the very real difference this will make to the lives of some of the lower-income families and children living around Leeds.”

Halewood also praised two volunteer projects in Liverpool – FACE and ReClaim – which he said have helped families claw back millions in unclaimed benefits.

Why we are urged to hate 'scroungers' when the real cheats are bankers

Backed by Leeds City Council, Bridge says the work of his advisers challenges the welfare stereotype that labels benefit claimants as scroungers.

“It confounds the common misconception of fraudulent benefit claimants,” he said. “Instead, we see that many people are not claiming what they are due.”

The project says the main reasons people don’t claim include embarrassment because programmes like Benefit Street and the language of politicians have increased the stigma of being “on benefits”.

Other people find the forms too difficult, are put off by bureaucracy or simply are never told by anyone that they might be entitled to benefits.

“I would say the stigma is the main reason people don’t claim,” says Kim Fowler, 32, one of the team of advisers.

“People are so apologetic when they come in. They are often ashamed – men crying because they are so embarrassed. They say, ‘I’m not a scrounger’, or ‘I’ve worked all my life’.

“I’m not judging anyone – I had a period in my life when I was on benefits myself and I know hard it is.

“But the portrayals of people on TV is a big factor. And the Government’s attitude to people on benefits seems to be trying to bring a culture of shame.

“Instead of helping, it’s about hitting them with a big stick.”

The spin is working. Last year an Ipsos Mori survey found the general public believed almost a quarter of all benefits were claimed fraudulently.

In fact, it is 34 times less than that amount. Official figures estimate fraud runs about 0.7%.

Compared to a 70% take-up rate on some benefits, that’s small fry. One of the people helped by the ­Children’s Centre project last week was Megan, a single mum with six-month-old twins.

A housing association tenant, she hasn’t ever claimed benefits, and until recently she earned £28,000 a year working in human resources.

Now on maternity leave, she is figuring out how to make life work as a lone parent of two young kids. Megan had come in to claim child benefit, but Kim showed her how tax credits could support her as she juggles fewer working hours and childcare.

“Even so, she was very reluctant,” Kim says. “She felt embarrassed, even though tax credits will actually keep her in work and mean she didn’t have to give up altogether due to childcare costs.”

Wednesday’s budget has of course changed things.

Kim estimates Megan has just lost around £1,988 support per year. Many of the people her team helps – parents of children under five, and pregnant women and their partners in some of the most deprived parts of Leeds – will have lost very similar amounts.

But even after George Osborne’s raid on the poor, billions a year will remain unclaimed.

A DWP spokesperson said: “We’re very clear about what benefits people can claim, advertising them through the Gov.uk website, at the Jobcentre and through stakeholder groups.”

This may be so but a mass take-up campaign would help cut family debt, stop loan sharks, reduce evictions and homelessness, and food and fuel poverty.

Meanwhile, taking up benefits directly affects neighbourhood economies, as low-income families usually spend their money locally.

Sadly it’s a campaign you will never hear from a Government whose plan to shrink the welfare state needs people on ­benefits to look like scroungers.