Labor has commissioned consulting giant Deloitte to help design a universal childcare system in Australia, launching a two-year study of demand and costs, as Anthony Albanese chases a political legacy to rival Medicare.

The government could redirect billions in spending on the childcare subsidy and introduce a daily flat fee for families. It will spend $10.4m on the research, with Deloitte required to assess service demands and collect data across the early childhood education system, with a report due before the next federal election.

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Findings by Deloitte would help the government “make further decisions about the pathway” toward universal childcare, a long-held goal of the prime minister and something he has described as a potential legacy.

The analysis would examine childcare wages and property costs, as well as the experience of operators, lobby groups and families, according to federal education department guidance seen by Guardian Australia.

Launched in early June, the Early Education Service Delivery Prices Project requires a data-based report to be handed to the government by early 2027, more than a year before the expected date of the next election in mid-2028.

It could lead to the introduction of a $10 flat fee for childcare services, similar to rules put in place in Canada in 2010. Work by the Productivity Commission suggests such a move would increase the total hours of work by single parents and secondary earners with young children by nearly 3% – the equivalent of about 17,000 additional full-time workers.

Higher tax rates have long acted as a disincentive for women to return to work. In February, parliament passed changes to eligibility rules for the childcare subsidy that mean parents will be guaranteed a minimum of three days of subsidised childcare regardless of how much they work or study.

The three-day guarantee begins from January 2026 for families earning up to about $530,000.

Early childhood education places have increased by 50% since 2013. Nearly half of all one-year-olds and about 90% of four-year-olds are enrolled in care.

Before next week’s economic reform roundtable, the Productivity Commission will on Wednesday release its latest interim report on how to deliver quality care more efficiently. It is expected to consider the role of childcare in the economy.

The childcare subsidy will cost the federal budget about $16.2bn this financial year, and is slated to rise to $18.4bn by 2028-29. With growth of about 5.5%, it is one of the big budget measures growing faster than nominal GDP.

“The big vision is certainly there,” Albanese said of universal childcare earlier this year. “That everyone would pay no more than a limited amount that was affordable – but we need to get there in stages.”

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In 2024, the Productivity Commission said removing the childcare subsidy and introducing a flat-fee model of $10 a day would cost $8.3bn annually.

Instead, it recommended one-child families earning less than $80,000 a year – and those with more children earning up to $140,000 a year – should receive three days a week of free childcare for 48 weeks of the year. That plan would cost $4.7bn annually if the existing subsidy was also limited to families with a combined income of less than $580,000.

Parliamentary Budget Office costings for 50 hours of universal care a week, with funding provided directly to providers, forecast a bill of $36bn over the forward estimates period – or about $126bn over a decade.

The federal treasurer, Jim Chalmers, said last week the total cost of a universal care system would depend on “how you went about it”.

“It doesn’t come cheap. You’ve got to make sure that any changes are affordable. If you look at the pressures on the budget, early childhood education is now one of the big half a dozen,” he said.

“We’ve indicated a willingness and an appetite to do more. We’ve got to work out how to make that affordable.”

A report from thinktank the Centre for Policy Development, released on Monday, called on Labor to commit to a 10-year plan for a universal system.

It said children who received quality early education were more likely to succeed at school, have better health outcomes, and participate in the workforce as adults.

About 95% of new operators joining the childcare system each year across Australia are private, suggesting the system would be largely for-profit without reform.