Welfare fraud and waste is never far from the top of the UK's news agenda – but the real figures often bear almost no resemblance to popular belief. The British public, for example, think around 27% of the welfare budget is lost of fraud, according to TUC research.

The Department for Work and Pensions' latest data on fraud and error in the benefit system shows a very different reality: fraud exists, but at a far lower level than the public believes – and is outweighed by errors from claimants and officials alike.

The overall figures show fraud and error are largely unchanged from last year. The DWP estimates £3.5bn has been overpaid due to errors and fraud in the system; 2.1 per cent of the overall benefit expenditure.

In total, 0.7% of total benefit expenditure was overpaid due to fraud: £1.2bn of the £166.8bn estimated final bill for welfare in 2012/13.

A further 0.9% of total benefit expenditure was overpaid following claimant errors, which occur when claimants fail to report changes in their circumstances or their when the information provided is incomplete or inaccurate, but there is no fraudulent intent from claimants.

The remaining overpayments were due to similar errors by officials, rather than claimants. The DWP and local authorities have been able to recover an estimated £890m.

But money doesn't just get overpaid: some welfare claimants don't get all the money that they're entitled to receive. £1.4bn is estimated to have been underpaid, primarily due to claimant errors, but 30%of underpayments were due to official errors.

When it comes to individual benefits, overpayments for income support have increased: 4.6 per cent, or £250m, of income support expenditure was overpaid, compared with 4.4 per cent the previous year. Income support cost £5.5bn to the State in 2012/13; 1.1 per cent of this figure was underpaid to claimants.

Figures for Jobseekers' Allowance (JSA) payments show that 4.2% of the expenditure was overpaid, compared with 4.6% the previous year. However, 69% of overpayments were due to fraud, an increase from 2011/12 where 63% of cases were from fraud. JSA payments totalled £5.3bn, which means an estimated £220m have been overpaid in the last year.

JSA overpayments due to official errors have fallen substantially over the last three years, accounting for 38% of JSA overpayments back in 2010/11 to 17% in the last year.

Housing benefit overpayments make up for more than a third of overall overpayments at £1.27bn, perhaps unsurprisingly given the higher total level of housing benefit. More overpayments have been made for housing benefit claimants since 2011/12, they made up 4.9% of the expenditure but now account for 5.3% of the housing benefit expenditure.

However, fraudulent claims have gone down, accounting for 27% of the overpayments, down from 31% the previous year.

Overall claimant error – not fraud – is the biggest source of loss in the welfare system, totally £1.6bn. Overpayments made due to official errors have gone down, dropping to £700m from £800m in 2010/11 and 2011/12.

The government launched a new system of Universal Credit last month in Manchester and Cheshire. When fully introduced, the government is hoping the system will cut fraud by a further £200m a year once it is fully implemented.

The minister for welfare reform, Lord Freud, assured the system would "revolutionise the welfare state" and "ensure that the unacceptable levels of fraud in the benefit system are reduced considerably."

However, early trials have sounded a note of caution: the system has been hit by delays and fears over the new IT system, leading some to fear it could cost far more than it saves.

What do you think of the latest welfare figures? Should more be made of them? And are there any other figures from the release we should highlight? Let us know in the comments below, or on Twitter @GuardianData