The future of the HS2 high-speed rail project has been thrown into doubt after the government launched a “go or no go” review into the proposed £55.7bn network, with a leading critic of the scheme as its joint author.

The transport secretary, Grant Shapps, said on Wednesday that the government needed “clear evidence” before deciding whether to go ahead.

The project is opposed by many Conservative party members and has been beset by questions over its escalating budget, with the prime minister, Boris Johnson, recently admitting he expected it to be “north of £100bn”.

Shapps said he had told the review to “just give us the facts … really, genuinely what it would cost to complete this project. Then we will know and we will be in a much better position to make the decision to go or no go by the end of the year.”

News of the review, which sources said could be completed by early October before the Brexit deadline, was met with dismay by business groups, unions and northern leaders, who called on the government to commit to the full line between London, Birmingham, Manchester and Leeds as soon as possible.

The review will be chaired by Douglas Oakervee, a retired engineer who briefly chaired HS2 Ltd and worked with Johnson when he was London mayor. His deputy, Lord Berkeley, a railway expert and Labour peer, is a critic of the project who has repeatedly challenged the Department for Transport’s (DfT) cost figures and warned that budgets were spiralling out of control.

Whitehall sources have been increasingly pessimistic about the project’s future following the appointment of another HS2 arch-critic, Andrew Gilligan, as a Downing Street transport adviser. And Dominic Cummings, Johnson’s senior adviser, was reported to have described HS2 as a “disaster zone” at a meeting last week.

The inquiry will examine whether the HS2 scheme linking London to Birmingham, Manchester and Leeds should be approved, amended or scrapped entirely.

An advisory panel to the review has been set up that includes leading rail figures, most of whom are supportive, but also features sceptics including the former Bank of England monetary policy committee member Andrew Sentance. The panel will have no right of veto on the final report.

Berkeley has previously suggested halting the scheme at Old Oak Common in London, rather than Euston, and cancelling work north of Crewe. He has also said the budget would spiral to double the official £55.7bn figure.

“One thing we’ve been promised is all the evidence, and I don’t believe the DfT has given all the honest evidence. There is so much that they haven’t disclosed. This project is probably 50% over [budget] already and they haven’t hardly started yet,” he said on Wednesday.

“I think [Boris Johnson] is keen that the DfT’s documentation is exposed. We’ve got to look at the evidence of the costs and also the potential revenue and some cost-benefits. And then we have to look at alternatives if it gets cancelled – and the costs of doing that.”

A review of the scheme was promised by Johnson in his campaign to become Conservative leader. The prime minister has said he is in favour of large infrastructure projects, although opposition to HS2 has been widespread among the Tory grassroots.

YouGov polling in May showed 49% of Conservative voters opposed building HS2, compared with 40% of the population as a whole.

Soon after taking office, Johnson promised to prioritise the building of a high-speed connection between Manchester and Leeds, at the heart of the Northern Powerhouse Rail scheme. However, transport and rail planners say the scheme is dependent on, rather than separate from, HS2.

The terms of reference say the review will inform the prime minister’s decision on “whether and how we proceed” with HS2. Phase one to Birmingham has already been approved by parliament, although Treasury funds for the major civil engineering contracts announced in 2017 have yet to be released under a “notice to proceed”.

The review will examine whether Northern Powerhouse Rail could be prioritised over building southern sections of HS2, or whether costs could be cut by modifying plans to build past Birmingham rather than jettisoning the whole project. That could mean reducing line speeds, or making Old Oak Common the London terminus, as Berkeley suggested.

Berkeley said he believed more rail capacity was needed, but added: “I’m opposed to saying it’s a good thing for the country and we should do it regardless of the costs.” But he added: “I share the view with [Johnson] that the investment needs to be in the north.”

While the mayor of Birmingham, Andy Street, is on the review advisory panel, northern leaders are not, although John Cridland, the chair of Transport for the North, is a member.

Andy Burnham, the mayor of Greater Manchester, said HS2 was vital, as well as Northern Powerhouse Rail. “People in the north will be wary of this review. There is no elected representative from the north on the review team and, too often, government promises to the north have proved to be about as reliable as our trains,” he said.

Tim Farron, the Liberal Democrat spokesman for the north, said “to even suggest cancelling HS2 is a slap in the face”. HS2 needed greater transparency and accountability, he said, but building it was “vital if we’re to rebalance our economy”.

Labour backs investment in high-speed rail, but Andy McDonald, the shadow transport secretary, said “improved governance of railway expansion was needed, not least over the HS2 project”. He said Labour wanted “an independent peer review to consider the project’s environmental and economic impact and its governance”.

Dr Adam Marshall, the director general of the British Chambers of Commerce, said HS2 would “attract investment to surrounding areas and rejuvenate local economies”. He added: “Business communities across the UK will be concerned about the potential for further delays to HS2.”

The CBI’s director of infrastructure, Tom Thackray, said the business message on HS2 was “clear-cut – back it, build it, benefit from it”.

The TUC general secretary, Frances O’Grady, said: “HS2 is vital to the development of the UK economy and there must be no question of it being scrapped.”

Anti-HS2 campaigners criticised the review, however, for being led by Oakervee, and “stuffed full of supporters of high-speed rail”. Joe Rukin, the campaign manager of Stop HS2, said: “If this is to be a genuine review, the government must cease all works immediately.”

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