The Chancellor says Treasury analysis has found that UK tax receipts would be £36bn-a-year lower after 15 years if Britain votes to leave the EU.
George Osborne and several other Cabinet ministers made the case for remaining in the EU by claiming what the cost of various alternatives would be for the UK.
Their claims are based on analysis by Treasury officials.
The £36bn figure is the amount the officials calculate the exchequer would lose if Britain was forced to enter a trade deal similar to that which Canada has recently negotiated.
The figure is the same as eight pence in the pound added to income tax.
The "Canadian model" is the scenario that many who want to leave say would be in Britain's best interest if the UK was to quit the bloc, including Mayor of London Boris Johnson.
But Mr Osborne said adopting it would also mean that individual households would end up £4,300 a year worse off.
Leave campaigners have dismissed the findings, with some, including MP Bernard Jenkin, describing Mr Osborne's use of Treasury staff as part of the remain campaign an "abuse".
Mr Osborne said: "Under any alternative, we'd trade less, do less business and receive less investment.
"And the price would be paid by British families. Wages would be lower and prices would be higher."
But Conservative MP and leave campaigner Andrea Leadsom told Sky News: "What today's report asks us to make is some enormous assumptions.
"For example, it doesn't take account of the potential for doing trade with the rest of the world.
"Let's face it; the EU accounts for only 17% of world GDP which means the other 83% is outside the EU, so that is where the growth potential lies."
Labour leader Jeremy Corbyn said he wanted more details on how Mr Osborne made the calculation.
"I'm not sure where he gets the figure from but, quite clearly, we are supporting the Remain campaign," Mr Corbyn told Sky News.
Former Chancellor and Out campaigner Lord Lamont told Sky News that Mr Osborne's forecast was "flimsy".
"The idea that someone can be absolutely certain about what things will look like after 14 years is frankly absurd," he said.
"I think they ought to be a bit careful on predicting disaster. At the very least, Britain will trade with the EU in the same way that other countries trade with the EU."
Meanwhile, the National Farmers' Union have declared that farmers' interests are best served by remaining in the EU, following a vote by the organisation's council.
The Royal College of Midwives has also announced it is in favour of staying in the EU, because it "has a vital role to play in ensuring decent and safe working conditions, and ensures a vibrant economy that allows the Government to invest in the NHS".
Mr Osborne, who made his speech at a research centre in Bristol, was flanked by Environment Secretary Liz Truss, Work and Pensions Secretary Stephen Crabb and Energy Secretary Amber Rudd, who each made the case against the different scenarios that could occur if Britain leaves the bloc.
Ms Truss said the Norway scenario - which assumes Britain would negotiate to join the wider EEA, like Norway, after leaving the EU - would lead to a 4% reduction in GDP per year after 15 years, meaning Britain's tax receipts would fall by £20bn a year and households would be £2,600-a-year worse off.
Mr Crabb said the WTO scenario - which is based on the idea that Britain would be able to set up trade agreements with EU member states using World Trade Organisation rules - would lead to GDP being 7.5% lower every year, would cost the country £45bn in tax and would cost households £5,200-a-year each.
It (Other OTC: ITGL - news) came as Labour also made its economic case for EU membership, with shadow chief secretary to the treasury Seema Malhotra appealing to older people to listen to the young on Europe and "take note of what they think is best for their future".