The Japanese ambassador has warned Theresa May that his country’s firms will quit Britain if a botched Brexit makes it “unprofitable” to stay.

Koji Tsuruoka laid bare growing nervousness about the impact of EU withdrawal on the Japanese car giants, banks and tech companies after meeting the Prime Minister in Downing Street.

“If there is no profitability of continuing operation in [the] UK, not Japanese only, no private company can continue operations,” Mr Tsuruoka said.

“So it is as simple as that. And this is all high stakes that I think all of us need to keep in mind.”

The warning comes after the Japanese government, in a leaked letter, called on Ms May to keep Britain in the EU single market and customs union and maintain a free flow of workers.

But the Prime Minister has vowed to pull the UK out of the EU’s economic structures and end free movement of citizens – although, in reality, those changes cannot take place until after a transitional period.

Speaking outside No 10, Mr Tsuruoka said Japanese companies were “enjoying their operations in the UK” and wished to stay – but that the decision rested on the outcome of the Brexit negotiations.

He added: “The question is whether the arrangements that will be reached between the two sides will allow the Japanese companies, who are willing and in some ways determined to continue to operate in the UK, to make that happen.

“This is contingent on a number of factors and there is not just one single factor that will be determining the decision.”

His country’s companies were “watching very closely” and badly needed “clarity and certainty, predictability”, Mr Tsuruoka said.

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However, the ambassador gave some backing to the beleaguered Prime Minister over claims the Cabinet is split over Brexit, saying: “I am not under that impression coming out of today’s meeting.

“I am under the impression that the UK Government is very firmly united behind the Prime Minister’s leadership in search and in pursuit of achieving the free, frictionless trade with the EU in a most ambitious manner.”

The comments came as sources said the second meeting this week of the “inner Cabinet” charged with agreeing a long-term Brexit plan broke up without achieving a breakthrough.

The 11-strong sub-committee spent just over two hours discussing future trade options – after failing to settle divisions over the Irish border and immigration on Wednesday.

The “roundtable” brought together cabinet ministers, including Chancellor Philip Hammond, Business Secretary Greg Clark and Trade Secretary Liam Fox, and top Japanese investors in the UK.

They included the heads of car giants Nissan, Honda, Toyota and Mitsubishi and train manufacturer Hitachi, as well as those of tech companies, energy firms and banks.

No 10 insisted the talks had focused on how to make the UK “an even more attractive destination for Japanese and international investment, as well as the UK-Japan trade and investment relationship”.

A spokesman said: “The Prime Minister reaffirmed the Government’s commitment to securing a new deep and special partnership with the EU as the UK leaves the EU.”

The business leaders had “agreed on the importance of the time-limited implementation period in providing clarity and certainty for people and businesses”, he added.