If the UK crashes out of the European Union without a deal at the end of the month, the government will be flooded by so many appeals for help from affected businesses that it will have to decide “who to save and who to let go”, a new report has warned.

The study by the Institute for Government said “no amount of preparation” by the government can eliminate the risks. Assessing ministers’ efforts to prepare the UK for no deal, it cited boxer Mike Tyson: “Everyone has a plan until they get punched in the mouth.”

Thousands of businesses can be expected to be hit by an unpredictable range of problems ranging from the imposition of new tariffs and trading barriers to congestion at ports and airports, falling demand, a collapse in sterling, tighter credit conditions, and changes to the rules on the movement of data and people.

And while the government may wish to “play Santa” by helping companies through a difficult period, it will have to be prepared to “play Scrooge”, picking and choosing firms to receive state support to avoid wasting taxpayers’ money. The ongoing costs for motor manufacturers, the service industry and other exporters will run into the tens of billions and “cannot be afforded”.

Boris Johnson insists he is ready to take the UK out of the EU without a deal on 31 October, and his no-deal supremo Michael Gove has led a £2bn drive to put preparations in place.

Boris Johnson and Brexit merchandise for sale at the Tory conference Show all 10 1 /10 Boris Johnson and Brexit merchandise for sale at the Tory conference Boris Johnson and Brexit merchandise for sale at the Tory conference A Boris Johnson doll for sale at the Conservative Party Conference in Manchester on 29 September PA Boris Johnson and Brexit merchandise for sale at the Tory conference Mugs with Boris Johnson's portrait for sale at the Conservative Party Conference in Manchester on 29 September AP Boris Johnson and Brexit merchandise for sale at the Tory conference A Boris Johnson themed T-shirt for sale at the Conservative Party Conference in Manchester on 29 September AFP/Getty Boris Johnson and Brexit merchandise for sale at the Tory conference Boris Johnson and other Conservative themed cards for sale at the Conservative Party Conference in Manchester on 29 September AP Boris Johnson and Brexit merchandise for sale at the Tory conference Boris Johnson posters for sale at the Conservative Party Conference in Manchester on 29 September EPA Boris Johnson and Brexit merchandise for sale at the Tory conference Copies of The Conservative newspaper are ready to be distributed during the Conservative Party conference on 30 September Getty Boris Johnson and Brexit merchandise for sale at the Tory conference "GET BREXIT DONE" mugs alongside other Conservative merchandise at the party conference in Manchester on 29 September PA Boris Johnson and Brexit merchandise for sale at the Tory conference Assorted Conservative merchandise for sale at the party conference in Manchester on 29 September PA Boris Johnson and Brexit merchandise for sale at the Tory conference Books about Jacob Rees-Mogg and Jeremy Corbyn for sale at the Conservative Party conference in Manchester on 29 September Getty Boris Johnson and Brexit merchandise for sale at the Tory conference A variety of books for sale at the Conservative Party conference in Manchester on 29 September Getty

But Giles Wilkes, the IFG’s senior fellow, said: “With a no-deal Brexit, the government would be pursuing a policy that its own analyses suggest will be very damaging to business.

“It is understandable that they want to play Santa and help UK plc over the ‘bumps in the road’. But faced with so many other calls on the public purse and with little idea of the medium-term direction of the economy, they will have to prepare to play Scrooge instead.

“Badly spent money might do more harm than good, propping up unviable companies and hurting competition.”

The report said that any industrial rescue effort after a no-deal departure would come against “a backdrop of steeply deteriorating public finances”.

“The government will be forced into impossible choices about which businesses and industries to save,” it said. “Without clear principles, the fight over subsidies will be swamped by politics.”

Ministers will face requests for help to cover short-term cash-flow problems and the costs of new bureaucratic burdens. But it can also be expected to receive appeals for support from companies rendered uncompetitive by changes in trading conditions that could be temporary or long-term, said the report.

Finance might be provided in the form of tax relief, grants, loan, bank guarantees or even direct equity stakes.

However, the IFG said: “With the scope of the effects of no deal being limitless, the first key decision for government is where it draws the line, so as to stop it being government’s job to support everyone.”

Given the “multiple sources of harm” to business in a no-deal scenario, it is “not even a theoretical possibility” to determine how many firms are at risk, said the think tank. And it warned that any attempt to draw up a list would inevitably favour big businesses over smaller enterprises.

“A great many businesses themselves do not yet know their own vulnerability and many would not know until after Brexit happened,” said the IFG. “The government cannot expect to either. There are over 200,000 UK businesses who trade internationally, and many more that might be indirectly affected.”

The IFG said the major conclusion of its study was that it would be “optimistic” to assume that the impact of no deal can be softened by making preparations for a finite period of turmoil.

The government has conducted trials to handle queues of lorries at Channel ports (Rex)

“The ongoing costs of a no-deal Brexit are so large that to talk of ameliorating them is often quite fruitless,” it said, citing the expected £2bn-a-year cost of export tariffs to the motor industry and the “much larger” hit to service exporters.

Because the length of time during which the UK would have to endure no-deal conditions is hard to know, the government “risks subjecting itself to an open-ended, financially ruinous commitment” if it seeks to cushion blows to these industries.

The IFG said ministers should draw up clear principles to identify the companies it will want to keep afloat and the requests for help that are not worth pursuing. It should hold back from a radical redesign of its industrial strategy at a time of disruption and financial constraint.

And it warned that “severe affordability constraints” will mean that measures used in the 2008 financial crisis – such as deferring tax payments and providing an enterprise finance guarantee for bank loans – may not be available.

“For some companies, the disruption brought about by a no-deal Brexit will be merely a passing inconvenience, or even an opportunity,” said the report. “For some others, it may signal an unavoidable need to exit a market altogether. Between these extremes lie the situations where the case for support is strongest.”

A government spokesman said: "The UK is getting ready for Brexit on 31 October. We want a deal, but we must be prepared for every eventuality.