The gloomy forecasts are part of the IFS Green Budget, looking at the challenges facing Chancellor Sajid Javid as he prepares for his first Budget.
The IFS's Mr Johnson said: "Given the extraordinary level of uncertainty and risks facing the economy and public finances, it [the government] should not be looking to offer further permanent overall tax giveaways in any forthcoming Budget.
"In the case of a no-deal Brexit, though, it should be implementing carefully targeted and temporary tax cuts and spending increases where it can effectively support the economy."
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But even before the cost of a possible no-deal Brexit is factored in, the think tank said the government was set to break its own spending rules.
The IFS forecasts that annual borrowing - the difference between what the government spends and what it receives through, for example, taxation - will top £50bn next year.
That will be about 2.3% of gross domestic product (GDP), a measure of national income. Under current spending rules the government can only borrow up to 2% of national income.
The think tank said the government's current plans for day-to-day spending next year are closer to the levels proposed by Labour's 2017 manifesto than plans laid out by the Conservative party at the time.
An HM Treasury spokesperson said: "September's spending round supported the people's priorities of health, education and the police within the existing fiscal rules, as we said it would be.
"Beyond that, the chancellor has already said that we will be reviewing the fiscal framework as we turn the page on austerity. In so doing, we will retain a fiscal anchor to public spending so that decisions are taken with a view to the long-term sustainability of the public finances."
A doubling in the annual budget deficit, leading, in relation to the size of the economy, to the highest government debt since the 1960s.
These are the new forecasts of the independent Institute for Fiscal Studies for how a no-deal Brexit is likely to drench the UK's public finances in red ink. Only on the extraordinary scale of the fiscal collapse of the 2008 financial crisis are these numbers modest.
On any ordinary scale they do matter - an annual deficit heading back up towards £100bn, and national debt closer to 90% of GDP for the first time in half a century.
And all this comes at a time where the institute concludes that the government is no longer taking its own fiscal rules seriously, borrowing more to spend more on public services even as the Treasury approaches its self-imposed limits.