The Department for Communities and Local Government has confirmed to the Guardian that it will publish details by the end of this month of how local authorities should assess the need for housing.

The plans, part of a package of housing measures, will be closely watched as a test of the prime minister’s appetite for enacting controversial domestic reforms.

They were slated for publication in July, and a press release drafted, but the launch was delayed at the last minute amid concerns some MPs could face criticism from constituents concerned about over-development.

The communities secretary, Sajid Javid, who has the backing of reformers in the Conservative party, would like to see housebuilding boosted significantly, particularly in high-cost areas, to halt the rapid increase in property prices that is leaving many people unable to afford a home.

In the housing white paper published in February, entitled Fixing Our Broken Housing Market, the government said: “Some local authorities can duck potentially difficult decisions, because they are free to come up with their own methodology for calculating ‘objectively assessed need’. So, we are going to consult on a new standard methodology for calculating ‘objectively assessed need’, and encourage councils to plan on this basis.”

Javid hopes by adopting an expansive approach, which includes data about the local housing market, he can kickstart redevelopment in areas where prices are rising fastest.

May’s resolve to tackle the problem may have been strengthened by the party’s poor showing among young people at the general election in June. A recent YouGov poll suggested that just 4% of 18-24-year-olds trust the Conservatives to deal with the issue of housing – against 44% for Labour.

Number 10 policymakers have been taking soundings from thinktanks and policy experts about proposals that might help to win back young voters.

According to official figures, homeowners could expect to pay about 7.6 times their annual earnings to buy a house in England and Wales in 2016, up from 3.6 times earnings in 1997.

The housing need test is one of a package of measures radical Conservatives believe will be necessary to tackle the challenge.

The Scottish Conservative leader, Ruth Davidson, in a speech focusing on housing policy in Scotland, said on Friday: “It is a bedrock of Conservative belief that we should encourage a property-owning democracy.

“Yet, increasingly, we now have something more akin to a property-owning oligarchy. Made up of lucky, mainly older, people who – by dint of having scaled the housing ladder – are now the ones who now control the country’s economic purse strings.”

George Freeman, chair of the Conservative policy forum, has also warned that young people risk rejecting capitalism if they have no chance of owning a home.

But Javid and and his allies are likely to find themselves pitched against Tory MPs and councillors wary of “planning blight”.

Andrew Mitchell, the former development secretary, publicly clashed with Javid over plans for a housing development in his Sutton Coldfield constituency.

May signalled on her trip to Japan that she wants to press ahead with domestic reform, as well as complete the Brexit negotiations.

She pointed to her Downing Street speech last year, in which she pledged to right, “burning injustices”, including the fact that “if you’re young, you’ll find it harder than ever before to own your own home”.

But watered-down corporate governance reforms published last week raised questions about whether May’s minority government will be willing to take on vested interests.

Housing campaigners urged the prime minister to be bold. Gill Payne, the executive director of public mpact at the National Housing Federation, said: “Getting this right will be a show of the strength of government’s commitment to building the homes the nation needs. Getting a consistent and accurate picture of housing need is really important – it cements into the local plan the number of homes that need to be delivered.”

She added: “Robust methodology will give a consistent and undisputable approach across the country.”

Polly Neate, the chief executive of Shelter, said: “We hope these changes will help to simplify and join up the way councils across the country assess housing need in their areas, and it’s vital that the new proposals work to deliver as many affordable homes as possible.

She added that Javid should tighten up the planning regime, to allow local authorities to exert more control over what can be built, where, rather than relying on the market to deliver.

“It’s important to remember that developers can still often build whatever they like, regardless of whether it meets what the council says is needed or not. The government must now take action to change this, by giving councils more power to get housing built that will meet the needs of their community.”

Successive governments have sought to make property ownership more affordable. Ambitious building targets have rarely been met, and George Osborne’s focus on subsidising mortgages through the help-to-buy scheme was criticised for fuelling the boom.