A future Labour government would build 125,000 new homes over the next five years by harnessing £5bn from a new ISA for first-time buyers announced in last month’s budget, Ed Miliband will announce.

The Labour leader, who was buoyed by a rise in his personal ratings after the seven-strong television election debate on Thursday night, will tell the party’s largest election rally so far that his plan will “pump prime” investment in housing.

In a speech on Saturday to more than 1,000 party supporters in Warrington, Miliband will say: “There’s no bigger symbol that our country doesn’t work for working people than young people not being able to get a start with a home of their own.

“We’re going to turn it round and build the kind of country in which we can all be proud. Investing in our future, investing in the next generation, giving hope back to young people and restoring the promise of Britain.”

Miliband is to propose that a Labour government would use the new help-to-buy Isa, announced by George Osborne in his budget last month, to create a £5bn future homes fund. This will allow an extra 125,000 homes to be built by 2020.

Banks and building societies that offer the Isas would be obliged to invest the funds in housebuilding. The government would underwrite every pound of the investment. But Labour would maintain the most attractive element of the chancellor’s scheme designed to attract first-time buyers – a £50 government top-up for every £200 invested in the Isas.

The Labour leader will say that his plan will tackle the central flaw in the Osborne scheme – that it stimulates demand for housing while doing nothing to increase supply.

Labour says the government has spent £6.6bn on schemes to stoke housing demand while neglecting housebuilding. The new fund would aim to “pump prime” supply after figures showed that the gap between supply and demand is on course to reach 2m homes by 2020. This will lead to an increase in the cost of an average home by £78,000 to £363,000.

Miliband regards the announcement as one of his most significant initiatives of the campaign as he aims to ensure that a Labour government transforms the rate of housebuilding, which has reached its lowest level since the 1920s. He believes it shows that Labour can adapt consumer-friendly measures to promote what he regards as progressive goals.

The scheme will be focused on housing growth areas, special new sites where local first-time buyers are given priority. Labour, which has pledged to ensure that 200,000 new homes a year are built by 2020, has already announced plans to force developers to build on land they own. Local authorities will be given powers to enforce a “use it or lose it” approach. A new generation of garden cities will be created to provide more than half a million homes.

Miliband will launch a scathing attack on the coalition for a negligent approach to housebuilding. The Labour leader will say: “Home ownership is now at its lowest level in 30 years. People are getting older and older before they can afford to buy their first home. There are now 11 million people who rent their homes, most of whom say they would like to buy. There are almost three and a half million young adults living with their parents – an increase of half a million in the last five years alone.

“So much of this is because the number of houses being built just isn’t keeping up with demand. Average house prices are now eight times the average wage.”

The announcement by Miliband comes amid increasing optimism about the Labour campaign in England and Wales, though there is deep concern about the SNP threat in Scotland.

Senior figures believe that the Labour leader has prevented the Tories from moving ahead in the polls after two strong performances in the consecutive television debates.

The figures acknowledge that Miliband did not achieve any knockout blows. But they say that he has performed well above his usual poll rating, stabilising his position and undermining Tory attempts to portray him as weak.