Public services such as health and education could face £36 billion of cuts if the country votes to leave the European Union, George Osborne has warned.
The Chancellor warned the price of Brexit would be paid by British families, who would be £4,300 a year worse off according to Treasury analysis.
As well as that long-term impact, he warned that in the short term the country would face a "profound economic shock and real instability".
Britain's economy would shrink by 6% by 2030 if the country replicated Canada's trading agreement with the EU, as advocated by Boris Johnson, according to the Chancellor.
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.
"The most likely result is that Britain would be poorer by £4,300 per household. That is £4,300 worse off every year, a bill paid year after year by the working people of Britain."
He said the analysis produced by the Treasury was "serious and sober" and showed "British families will pay a heavy economic price if we leave the EU."
Mr Osborne rejected the claims of Leave campaigners that the country would benefit from the savings made by not contributing to Brussels' coffers.
Speaking in Bristol he said: "Don't believe the flimsy claim that at least we would get some money back by not paying our 1p on every £1 we raise in taxes to the European budget.
"We'd lose tens of billions of pounds in money for our public services, because our economy would be smaller and our families poorer.
"The most likely bill our public services would pay for leaving the EU is £36 billion.
"That's the equivalent of 8p on the basic rate of income tax."
Flanked by Cabinet ministers Liz Truss, Stephen Crabb and Amber Rudd, Mr Osborne said the June 23 referendum represented "the biggest decision for a generation - one that will have profound consequences for our economy, living standards and Britain's role in the world".
Voters should ask themselves "Are you better off or worse off if Britain leaves the EU? Does your family get more money or less? And is there more money or less available to your Government to pay for public services and tax cuts?"
Mr Osborne said it was "a complete fantasy" to suggest that the UK would be able to negotiate access to the single market without agreeing to accept the costs and obligations of EU membership.
"How could other European countries give us a better deal than they have given themselves?" he asked.
This meant the UK would have three options for its future relations with the EU - either for the status currently enjoyed by Norway, which makes payments to the EU and accepts free movement in return for access to the single market, or a bilateral free trade deal of the kind obtained by Canada, or gaining more limited access under the rules of the World Trade Organisation.
Meanwhile, the Chancellor claimed that the reforms negotiated by Prime Minister David Cameron offered a "huge prize" for the UK, which could increase its GDP by 4% over the coming years and would be worth thousands of pounds to the average household.
The 200-page Treasury document uses a complex model to examine the potential impact of three different possibilities for the UK by 2030 after Brexit - a Norwegian-style membership of the European Economic Area, the Canadian-style negotiated bilateral trade deal, and the fallback option of World Trade Organisation (WTO) rules.
The analysis suggests that the EEA style approach would see GDP fall by between 3.4% and 4.3% - a central estimate of 3.8% - in 2015 terms.
That would leave households £2,600 poorer, based on the number of families in 2015.
The figures used by Mr Osborne are based on a Canadian-style deal, which would see GDP drop by between 4.6% and 7.8%, with a central estimate of 6.2%, resulting in the £4,300 per household impact.
If there was no deal with the EU, and the UK fell back on WTO rules, the economy would suffer by between 5.4% and 9.5%, with a central estimate of a 7.5% fall - hitting each household by £5,200.
The analysis suggests that EEA membership would result in £20 billion lower public sector net receipts, the Canadian deal would leave the public sector £36 billion worse off and the WTO deal could mean £45 billion less for services.
Answering questions following his speech, Mr Osborne said the Treasury analysis had been welcomed by leading economists, adding: "You can't name a single ally of Britain, a single major trading partner of Britain, a single credible international financial organisation, which is saying it would be a good idea for Britain to leave the EU."
In an apparent swipe at pro-Brexit London mayor Boris Johnson - who famously said that his policy on cake was "pro-having it and pro-eating it" - the Chancellor said: "What I don't think you can claim is that somehow Britain can have its cake and eat it, that we would have all the benefits of EU membership without the costs and obligations. That is not credible.
"Indeed, the most prominent campaigners for us leaving the EU do admit there would be an economic shock and that jobs would be put at risk."
TUC general secretary Frances O'Grady described the Treasury figures as "a sobering reality check", adding: "For working people the message is clear: vote leave, get poorer.
"Brexit campaigners have yet to come up with any convincing answers for how a post-Brexit economy would function. They have nothing to offer but a future of lower pay and fewer jobs."
But Sam Bowman, executive director of the Adam Smith Institute thinktank, said: "The Treasury's numbers are based on a scenario of Britain coming to a limited Canada-style free trade agreement with the EU, which would indeed be a poor outcome.
"The UK is far too deeply economically integrated with the EU for such a limited trade arrangement to work. But this is very unlikely to be what does happen. It is only likely if we think the Government and civil service would seek a post-Brexit deal that they themselves believe to be against Britain's interests."