The number of working households forced to rely on housing benefit since the recession began in 2008 has doubled – a trend that will lead to a million earners being dependent on welfare to keep a roof over their heads by the next election, according to a report.

The Home Truths study by the National Housing Federation found that in May 2012 there were 903,440 working recipients of housing benefits – more than double the figure for November 2008 and a jump that signifies an alarming rise in in-work poverty.

As private rents rise faster than wages, another 10,000 working people a month need housing benefit to afford their rent. By the next election, the study warns, 1.2 million "strivers" will only be able to stay in their homes through welfare payments.

The federation's analysis is that housing is becoming unaffordable as supply is outpaced by demand. The number of households in Britain is growing three times as fast as the number of homes being built.

In England by 2018 the average weekly rent will be £245, up from today's £181, a leap of 35%, the study says. The lingering recession means house prices will fall next year but then rise sharply. By 2018 homes in England will cost on average £292,060, almost £60,000 more than today.