Britain’s failure to build affordable homes has led to a soaring housing-benefit bill – with half a million more people now relying on state handouts to pay their rent than when the coalition came to power, a damning new analysis reveals.

The coalition’s crackdown on welfare has failed to prevent an explosion in the number of people relying on state help in recent years, with a total of five million people now claiming housing benefits. And with 1.8 million on waiting lists for social housing, hundreds of thousands more have, instead of escaping welfare dependency, fallen into the hands of private landlords charging increasingly exorbitant rents.

Spending on housing benefit has risen by £650m a year on average since 2009-10, and at a faster rate than during Labour’s 13 years in power, a new analysis of official Department for Work and Pensions figures finds. The annual housing benefit bill is expected to hit £25bn by 2017.

A major cause of the ballooning bill, according to experts, is the dearth of affordable housing. The number of affordable homes built in 2013-14 was the lowest in a decade – despite the UK’s population rising by five million over the past 12 years, a rate of growth unequalled anywhere in Europe.

As demand has grown, private landlords have hugely increased rents. Commuter areas outside London such as Surrey Heath and Elmbridge saw rises of 14% last year.

The huge increase in housing-benefit claimants has been despite the new coalition government’s announcement of a war on the “out of control” benefit budget in 2010. Proposals included the benefit cap, introduced in April 2011 for new claimants, which saw the maximum amount a claimant could receive limited to £500 a week for families with children and £350 for individuals.

Spending on housing benefit did fall marginally, by £150m in real terms, in 2013-14, compared with the previous financial year. Around 28,000 fewer people claimed housing benefit, reducing the numbers from 5,053,000 to 5,025,000. Yet in the period between 2009-10 and 2013-14 as a whole there was an increase of 478,000 in the number of claimants.

The Observer has learned that chancellor George Osborne will use his 2015 budget on 18 March to announce an extension of the Help to Buy scheme, under which the government lends up to 20% of the cost of a new-build home in a bid to stimulate building. He will also propose a reform of the compulsory purchase laws to enable property developers to respond more swiftly to changes in demand.

However, John Healey MP, a former Labour Treasury minister who has analysed the figures on housing benefit take-up, said the government had failed to tackle early enough the central problem of a lack of homes. Alongside an increase in the number of people renting privately, Healey further claimed the government’s policy to increase rents in council and housing association homes to up to 80% of the local market rent had been disastrous.

The MP said: “These figures show that David Cameron has completely failed to curb spending on housing benefit. He has made life a misery for people on low incomes by cutting entitlements back to the bone, but the housing benefit bill has continued to rise.

“The reasons for his failure are clear. Inaction on low pay and high rents has meant that wages haven’t kept pace with housing costs, and so more people are struggling to afford their rent. This has meant huge growth in the number of working people now receiving housing benefit to help make ends meet.

“But the housing benefit bill is also being driven up by ministers’ decision to cut investment and hike rents in council and housing association homes.”

During the Blair-Brown years, 1997-2010, there was a reduction in the number of people claiming housing benefit of 193,000, although all the progress on those numbers was made under the Blair administration.

A DWP spokesman said: “The housing benefit bill was spiralling out of control in the years up to 2010, increasing by 50% in a decade and forecast to rise further. Housing benefit spend has now actually fallen and our actions will have saved the taxpayer up to £6bn by the end of this parliament.”