Nissan was convinced to stay in the UK with a promise of no tariffs or extra bureaucratic burdens on the car industry after Brexit, the business secretary has finally revealed, prompting fears that sector-by-sector deals could cost the taxpayer “colossal amounts of money”.

Greg Clark caved in after four days of pressure in an interview on Sunday to reveal some details of how the government convinced the Japanese manufacturer to produce a fleet of new vehicles at its Sunderland plant. The Tory minister said he wrote to Nissan with a series of four assurances as he went “all out” to allay concerns about Brexit, promising that the government was confident of securing a deal that would keep the car industry competitive.

“Our intention, our negotiating remit, when it comes to the discussions with our European partners, is to have a constructive dialogue and look for the common interest here,” Clark told the BBC’s Andrew Marr Show. “Our objective would be to ensure we have continued access to the markets in Europe and vice versa without tariffs and bureaucratic impediments, and that is how we will approach those negotiations.” He suggested that this applied to the car industry in general and possibly to other major sectors of UK business.

That suggests No 10 is seeking a free trade relationship for the automotive industry that at least brings benefits similar to membership of the single market and customs union. Theresa May has however said she wants greater immigration controls and freedom from the oversight of the European court of justice – a combination that Brussels politicians have repeatedly said is unachievable.

The admission prompted questions about the financial cost of protecting the industry from the impact of Brexit. Nick Clegg, the former deputy prime minister, wrote to Clark, his former cabinet office colleague, warning that a series of deals for different industry sectors could cost the taxpayer “colossal amounts of money” in subsidies.

The Liberal Democrats’ spokesman on Brexit also raised the prospect that the UK might have to continue paying billions into the EU budget in order to secure preferential trading terms with the single market for certain industries or all of them.

On the promise relating to Brexit, Clark told Marr that the UK could not know the outcome of negotiations with the other 27 members but that it was “very important that we make a commitment to keep competitive the UK industry” through the government’s industrial strategy.

The business secretary said there was no specific promise to compensate Nissan if it did face tariffs, because that would not be allowed under competition laws, but the letter of comfort had been sufficient to persuade the carmaker to continue investing in north-east England. The letter contained promises of a continuation of funds for training, skills and scientific research, and regional relocation grants.

In his letter to Clark, Clegg said the news that Nissan was staying was welcome, but questioned whether the assurances were “part of a planned strategy with a desired endpoint or a one-off concession which shows those that shout the loudest get the best deal from ministers”.

Clegg, who is playing a leading role in the Open Britain campaign group, called for more clarity on what it meant for No 10’s wider Brexit strategy.

“Any assurances given about our future relationship with the customs union and the single market would go to the very heart of the Brexit negotiations, revealing whether the government is intending to stay within either, or whether you intend to negotiate a patchwork of carve-outs, subsidies and sectoral arrangements, which will create winners and losers and may cost the taxpayer colossal amounts of money,” he said.

Clark’s interview led to further criticism that the government had been telling industry more about No 10’s negotiating aims than the UK electorate. Clive Lewis, the shadow business secretary, said: “While we welcome the commitment to securing tariff-free trade for the automotive sector, Greg Clark has raised more questions than he’s answered. What about other manufacturing sectors, or services, which, let’s not forget, account for 90% of our economy? Nor has the government said anything about how is tariff-free access is going to be achieved.”

Keir Starmer, the shadow Brexit secretary, told ITV’s Peston on Sunday that Nissan “has been told more about it than we have in parliament”, adding that the government had “got to come clean”. The senior Labour MP also accused the prime minister of prioritising greater immigration controls over the health of the UK economy as she headed towards triggering Brexit early next year.

He said he intended to ask an urgent question in the House of Commons on Monday to urge ministers to reveal any guarantees that they may have given. “There may be a financial element to it – I accept that. They say no money is changing hands,” he told Peston. “I don’t know. We need to know and I’m going to try and raise this in parliament … because something has been said.

“It’s good Nissan are investing, of course it’s good, but there are other businesses up and down the country of every size and every sort that need [reassurance].”

Mike Hawes, the chief executive of the Society of Motor Manufacturers and Traders, said he was “greatly encouraged” by Clark’s comments.

“It is important government makes it a priority to safeguard the competitiveness of this important and globally successful sector as we leave the EU,” he said.

“This means maintaining a competitive business environment, ensuring talent can be recruited from abroad and securing the benefits we currently enjoy in the single market, including tariff-free trade unhindered by any customs bureaucracy.”

Terry Scuoler, chief executive of manufacturers’ organisation EEF, said: “Whatever terms have been agreed it’s good for the north-east that investment has been secured and potentially for the wider motor industry.

“Manufacturers want to secure access to the single market on the best terms possible and we support any efforts that move in this direction.”

A key question for May will be whether she is willing for the UK to continue paying into the EU budget in order to secure tariff-free trade without bureaucratic customs checks.

Nadhim Zahawi, a leading Brexit supporter and Conservative MP for Stratford-upon-Avon, wrote in the Mail on Sunday that paying a proportion of the UK’s annual £8.5bn would be worth it for favourable trading arrangements combined with freedom from the EU’s immigration rules and the jurisdiction of its courts.

“I was one of those who campaigned to leave, but the government should be absolutely clear that our motive is not for the European Union to fail – we just don’t think it is right for us,” he wrote.

“That is why we should pay a proportion of the £8.5bn that we will save through leaving back into its budget. We should help bridge some of the EU’s funding gap, but only on the condition that the EU delivers our demand of providing British businesses with tariff-free access to the single market.”