The government has come under renewed pressure to reveal details of the commitments it gave Nissan ahead of the Japanese carmaker’s announcement that it would build two new models in Britain.

Chuka Umunna, the former shadow business secretary and a leading member of the Open Britain campaign group, has written to the cabinet secretary, Sir Jeremy Heywood, asking him to reveal whether public money was offered to Nissan to alleviate the impact of potential trade tariffs when Britain leaves the European Union.

“Other vital sectors of our economy, such as the aerospace industry, agriculture and the financial services industries are likewise dependent on our place within the single market and customs union, which minimise tariff and non-tariff barriers to an unparalleled degree. If the UK were to leave both, there would be a profoundly damaging impact on these and other sectors,” Umunna wrote.

“It is vital to understand, therefore, the assurances that were given that determined Nissan’s decision.”

The letter from the Labour MP comes after Anna Soubry, a former business minister, revealed that Nissan had previously suggested to her that it could move its factories to France if it was not protected from trade tariffs.

Soubry said that No 10 must have privately told Nissan that Britain was remaining in the EU customs union, or promised mitigation against any future tariffs, before the car firm announced plans to build two new models in the UK.

It is understood that the government provided a “letter of comfort” to Nissan promising that the UK car industry would remain competitive after Brexit. Ministers, however, would neither confirm nor deny whether such a letter had been sent.

Sources said the letter was understood to give an undertaking that Nissan would not face “additional costs” after the UK leaves the EU, implying that the taxpayer could be liable for subsidising the car industry in the event of tariffs being imposed on automotive exports.

Umunna’s letter asks Heywood to settle speculation over whether public money could be used to compensate Nissan – whether directly or indirectly – and whether ministers had given the company inside information about their plans for negotiating the UK’s future position in the EU’s customs union or single market.

“I am of course supportive of the government’s aim to protect our manufacturing base, but it seems extraordinary that the government would reveal elements of its negotiating strategy to multinational companies when it is at the same time doing its best to keep parliament and the public in the dark,” his letter says.

“To ensure there is rigorous public scrutiny of government decision-making, I urge you to immediately publish details of the commitments, written or otherwise, given by Downing Street and the rest of the government to Nissan.”

Nissan committed to assembling its new Qashqai and X-Trail models at its Sunderland plant.