Whoever becomes the next prime minister will commit to HS2, the business secretary has said, despite the frontrunner Boris Johnson being opposed to the scheme.

Greg Clark described the £56bn rail project as “crucially important” and said it would have a “transformational” impact on the economy and communities across England.

Yet Johnson, who has been critical of HS2, said at the weekend he had already commissioned a review of the high-speed line. He told a Tory leadership hustings that he had asked Douglas Oakervee, the original chair of Crossrail, to examine the business case for HS2 “and to think about whether and how we proceed”.

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In an interview with the Guardian in Manchester, Clark said he believed the next prime minister would ultimately back the controversial project, which will connect London to Leeds and Manchester via Birmingham.

Asked if HS2 would definitely go ahead under the new leader, Clark said: “Yes. You saw what happened in 2013 when Ed Balls as shadow chancellor questioned whether a Labour government would scrap HS2. You had quite an impressive reaction from the leaders of all of the northern cities, who virtually marched on Downing Street and said: ‘It is absolutely essential to our future.’

“It is so important for the whole country, not just the north, that we have the type of connections that other modern economies have.”

He added: “If any of the leadership contenders come and talk to not just the civic leaders but the business leaders, they will see how important this is, not just for the future, but now. If you go to Birmingham you already see, in central Birmingham around Curzon Street, you will see city streets are already being regenerated now at the prospect [of HS2]. That can’t be taken away from them.”

Asked if Johnson and other candidates’ opposition to HS2 showed they were out of touch with the north, Clark said: “I remember when Boris was mayor of London. He knows the transformational value of good transport connections, not just for the economic health of an area but for communities as well.

“I think you will see – and contenders should be tested on this – they will be questioned on this by the leaders of our great northern cities and they will see how crucially important it is.”

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Clark’s comments came as political leaders from across the north wrote to the six remaining Tory leadership contenders to express alarm at the “damaging levels of uncertainty” surrounding the future of the project, for which construction work is already under way.

The letter, signed by leaders representing a combined population of 15.4 million people, urged the contenders to publicly back HS2 and Northern Powerhouse Rail, a £39bn transpennine rail line that would link to the high-speed network.

Sir Richard Leese, the leader of Manchester city council, said: “This is a once-in-a-generation opportunity for us which, if successful, will secure the future economic prosperity of northern communities. We must seize it with both hands.”