Leaving the European Union could mean £36 billion less to spend on public services, according to a Treasury analysis launched by George Osborne.
The Chancellor warned that British families would pay a "heavy economic price" if the country votes to break from Brussels on June 23, with the UK left permanently poorer.
The 200-page analysis produced by officials in Mr Osborne's department was mocked by Brexit campaigners and branded "dodgy", but the Chancellor insisted it was a "serious and sober analysis".
Mr Osborne also faced questions over the assumption used in the document that net migration would fall to 185,000 a year from 2021 onwards - far in excess of the Government's goal of reducing it to the "tens of thousands" - with Leave supporters arguing that the Treasury had failed to take into account the costs of coping with an ever-growing population.
The Treasury analysis examined three potential options for the UK if it left the EU - the status currently enjoyed by Norway, which makes payments to the EU and accepts free movement in return for access to the single market, a bilateral free trade deal of the kind obtained by Canada, or a relationship under the rules of the World Trade Organisation.
The Chancellor focused his assessment on the Canada-style model, which has previously been championed by Boris Johnson.
Under the terms of a Canadian-style bilateral trade deal with Brussels, the economy would be 6.2% smaller by 2030, the equivalent of £4,300 per household, the analysis suggested.
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."
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."
The Treasury document suggests that the Norway-style approach would see GDP fall by a central estimate of 3.8% in 2015 terms, the equivalent of £2,600 per household.
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 Norwegian-style European Economic Area membership would result in £20 billion lower public sector net receipts, the Canadian approach would leave the public sector £36 billion worse off and the WTO route could mean £45 billion less for services.
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 Mr 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."
Brexit-backing former chancellor Lord Lamont of Lerwick dismissed the report's projections.
"They say economists put a decimal point in their forecasts to show that they have a sense of humour," he said. "The Chancellor has endorsed a forecast which looks 14 years ahead and predicts a fall in GDP of less than 0.5 per cent a year – well within the margin of error. Few forecasts are right for 14 months, let alone 14 years. Such precision is spurious, and entirely unbelievable."
Pro-Brexit minister Andrea Leadsom, who had served in the Treasury under Mr Osborne, claimed the document was "extraordinarily biased" because it failed to consider the impact of continued high migration.
"A much fairer way to present this argument would be to also look at the impact if we remain in on further migration, further pressure on public services, the impact on security and so on," she said. "You have got to present a balanced view."
The Energy Minister mocked the report's long-term prediction, telling BBC Radio 4's World at One: "It's extraordinary to have such an accurate central figure and it implies a clarity of crystal-ball gazing that even I, as a fully paid up witch, couldn't possibly presume."
Matthew Elliott, chief executive of the Vote Leave campaign said the report's figures were "deeply flawed".