Leading Leave campaigners have set out a blueprint for an immigration system based on the Australian model in the event of a Brexit. Prospective migrants from the EU would be required to speak good English and have the relevant skills for the job in question, according to a statement from Conservative Eurosceptics Boris Johnson, Michael Gove, Priti Patel and Labour's Gisela Stuart.

With little over three weeks to go before the EU referendum on 23 June, the prominent Out campaigners pledge to "create a genuine Australian-style points-based immigration system" before the next general election, due in 2020. The points proposal comes just days after the leading Leave figures vowed to scrap VAT on fuel to help the poorest UK households on 30 May.

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The announcements effectively amount to an alternative proposal to that tabled by David Cameron as polls indicate Leave is gaining momentum. According to two Guardian/ICM polls, 52% of voters are backing a Brexit compared to 48% who support Remain. Meanwhile, a YouGov survey for the Times has both sides deadlocked on 41%.

After a vote to leave the EU, "the automatic right of all EU citizens to come to live and work in the UK will end, as will EU control over vital aspects of our social security system," Gove and Johnson say. "EU citizens will be subject to legislation made by those we elect in Westminster, not in Brussels. We could then create fairness between EU citizens and others, including those from Commonwealth countries," they add.

The Australian system grants migrants a skilled migration visa if they pass a points test based on their nominated occupation, English language ability, past employment and education. EU migrants already in Britain would be granted indefinite leave, the Leave campaigners say.

"Those seeking entry for work or study should be admitted on the basis of their skills without discrimination on the ground of nationality. To gain the right to work, economic migrants will have to be suitable for the job in question. For relevant jobs, we will be able to ensure that all those who come have the ability to speak good English," the statement adds.

Immigration is a key issue in the EU referendum debate, after figures last week showed that net migration to the UK has risen to 333,000 in 2015, according to estimates from the Office for National Statistics. The Tory trio seized on the party's election commitment to slash net immigration to the tens of thousands and said it was time for a change of tactics to deliver on the promise.

"This promise is plainly not achievable as long as the UK is a member of the EU and the failure to keep it is corrosive of public trust in politics," they say.

In their statement, the Eurosceptics also warn that the country will not be able to cope with the "particular strain on public services" if current levels of net immigration from the EU continue. "Class sizes will rise and waiting lists will lengthen if we don't tackle free movement. As the euro crisis continues, more people from southern Europe will want to escape unemployment and austerity in their countries by coming to the UK. Their arrival will put further strain on schools and hospitals," the statement says.

But Britain Stronger in Europe – the official Vote Leave opposition group – dismissed the proposal, saying it "will not work" and pointed to Australia's migration levels. "Vote Leave's proposal could put up immigration and it would wreck our economy, as it involves leaving Europe's single market," said Will Straw, executive director of Britain Stronger in Europe.

"Australia, who have a points based immigration system, have twice as many migrants per head as the UK," he added. "Economic experts are agreed that leaving the Single Market would lead to recession - costing jobs and raising prices."

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