The budget office cautioned that it was unlikely a large number of people on Commonwealth Rent Assistance – which the government has increased by more than a quarter over the past two years – would use the policy as they were on low incomes with relatively small super balances.

It found up to a quarter of people who would use the super scheme would have bought a home regardless. The budget office also noted that the research assumed all participants would be able to service a mortgage, stating that as its work included people close to retirement age, this might have inflated the assumed take-up rate.

The budget office was not asked to look at other impacts on the budget, such as the number of additional people who would require a pension if they had used up their super.

Bragg will also say the government’s housing agenda, including its Help to Buy and Build to Rent policies, which both face defeat in the Senate, is failing to support homeownership.

“Labor’s rent-forever plan is little more than a Ponzi scheme where Australians will spend their working life paying super, and their retirement paying rent,” he will say.

The Help to Buy scheme seeks to allow the government to contribute up to 40 per cent of the purchase price of a new home, or 30 per cent for an existing home, for up to 10,000 selected applicants a year. It is based on pre-existing state government policies.

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Under the government’s Build to Rent plan, tax incentives, including a reduction in the final withholding tax on properties held by institutional investors, would be made available for new rental construction. Ten per cent of properties would have to be offered at an “affordable” rate, which is defined as 75 per cent of the going market rate.

On Monday, Albanese and Housing Minister Clare O’Neil revealed the first 13,742 homes to be financed by the government’s $10 billion Housing Australia Future Fund would soon get under way.

The government has rejected the Coalition’s super-for-housing policy, arguing it would drive demand rather than add to the supply of new homes. Research commissioned by the Super Members Council this year found it could push up median house prices by as much as 9 per cent, including by $80,000 in Sydney and almost $70,000 in Melbourne.

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Bragg will dismiss suggestions of massive price or rent increases as “Dr Evil-like predictions of doom and gloom”.

“In reality, it would be an optional scheme that would be open to those to use in addition to any additional savings they may have,” he will argue.

Independent MP Allegra Spender, who is working on her own tax green paper, said the Coalition and Greens should back the government’s Help to Buy plan.

She said the scheme was not only for first-time buyers, arguing it would help older Australians, including divorced women, who risked becoming “renting retirees”.

“This scheme must be coupled with broader action to boost housing supply. This includes removing the barriers to construction worker immigration, slowing infrastructure builds to lower construction costs, tax reform and stronger incentives for states and local government to unlock supply,” she said.

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