Ralf Speth says he cannot be sure any UK plants will continue to operate after Brexit

Britain’s biggest car manufacturer, Jaguar Land Rover, has launched a blistering attack on Theresa May’s handling of Brexit as leading Eurosceptics claim there is “nothing to fear” about crashing out of the EU without a deal.

Ralf Speth, the chief executive, told the prime minister that the company’s factories faced grinding to a halt and “tens of thousands” of jobs in the sector could be lost if she failed to reach an agreement with Brussels.

In a surprise intervention at a landmark car industry summit organised by the government, he described the prospect of a cliff-edge break with the EU as “horrifying”, warning that if wrong decisions were taken now it could result in the “worst of times” for the UK.

He stressed the company was “firmly committed” to the UK but warned that a hard Brexit would cost it £1.2bn a year, wiping out profits. “What decisions will we be forced to make if Brexit means not merely that costs go up, but that we cannot physically build cars on time and on budget in the UK?”

It follows similar warnings from other industry chiefs, including Airbus and BMW, about the potentially damaging consequences of Britain’s decision to leave the EU.

May, who was waiting backstage as Speth delivered his speech, did not mention Brexit in her own address to the Birmingham summit immediately after his.

Downing Street said one of the key elements of May’s Chequers plan was to try to protect the industry’s supply chains with the EU, with the common rulebook proposal helping ensure frictionless trade. The issue came up at a round table discussion later.

Speth told the conference that friction at the border could jeopardise production to the value of £60m a day. He also warned that traffic jams on the approach to Dover meant that “bluntly, we will not be able to build cars”.

He pointed out it was now cheaper for the company to make cars in Slovakia than Britain. “Six months from Brexit and uncertainty means that many companies are being forced to make decisions about their businesses that will not be reversed, whatever the outcome, just to survive,” he added.

May is holding a “no deal” cabinet meeting on Thursday at which ministers will discuss plans in the event of the government failing to reach a deal with Brussels. No 10 insiders, however, are growing increasingly confident of striking an agreement.

Leading Brexiters on Tuesday pushed back against claims that their campaign to “chuck Chequers” was going off the rails, and endorsed an alternative proposal that resulted in the UK crashing out on to World Trade Organisation (WTO) rules.

Jacob Rees-Mogg, the chair of the pro-Brexit European Research Group (ERG), said there was “nothing to fear” from a no-deal scenario after the pro-Brexit economist Patrick Minford claimed it could boost Treasury revenues by £80m a year.

Rees-Mogg said, however, that he would still prefer the government to strike a Canada-plus-style trade deal with Brussels to retain the benefits of leaving on “the most friendly terms we can manage”.

At a crowded event at the House of Commons, Boris Johnson made a surprise appearance alongside other senior Brexiters, including David Davis and Iain Duncan Smith, to back the plans drawn up by Economists for Free Trade.

The former foreign secretary claimed that the Chequers plan would be “substantially worse” than the status quo for British businesses and that he had a “particular economic objection” to firms being tied to the single market.

The Brexiters’ campaign has been overshadowed by interventions from Johnson, who described the Chequers plan as a “suicide vest”, as well as his tumultuous personal life and renewed questions over his ambitions to lead the Tory party.

When asked if he would be prepared to launch a leadership bid to prevent May pushing ahead with her plans, he pointed at a colleague and said: “What he said.”

The former Brexit secretary Steve Baker had just told the room: “Isn’t the future of this country about more than personalities? This event is not about who the prime minister of this country ought to be, it’s about policy.”

Rees-Mogg confirmed he would vote against the Chequers deal in the Commons but said he hoped the government would not make it a confidence matter, adding that to conflate the two would be a mistake.

The prime minister has challenged the Brexiters to publish their alternative plan but ERG members appear to have struggled to agree on how to avoid a hard border in Ireland, a main sticking point in discussions with Brussels.

The group is expected on Wednesday to set out a proposed solution to the border problem, which Rees-Mogg said “any reasonable person” would accept. It could include tax inspectors conducting spot checks in factories on goods for export.

At the Lords economic affairs committee, the chancellor, Philip Hammond, claimed that the logic behind Minford’s WTO proposal was unsustainable and “wildly out of line” with the prevailing economic consensus.

He said Britain would still have to meet its outstanding financial obligations to the EU if no deal was reached, although the amount would have to be negotiated with Brussels later.

In a sign on Tuesday night that hard Brexiter unhappiness about May’s leadership and insistence on Chequers had intensified, a meeting of the ERG attended by around 50 MPs openly discussed trying to force out the prime minister although it is not clear they have the numbers or enthusiasm to force a confidence vote.