The HS2 high-speed rail project will cost up to £30bn more than expected, an internal review has warned – raising fresh questions over whether Boris Johnson will axe it.

The final bill for building the network is likely to be between £70bn and £85bn – not the £56bn budgeted – HS2’s new chairman is believed to have told the Department for Transport (DfT).

The warning, revealed by the Financial Times, follows a series of delays, concerns over poor management and allegations by whistleblowers that parliament was misled on the cost of land purchases.

The project is strongly supported by council chiefs in the north and midlands, which would be connected to London by trains capable of travelling at 250mph.

But Mr Johnson, who is near-certain to be prime minister next week, has criticised the way costs are “spiralling out of control” and refused to guarantee it will go ahead as planned.

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The Tory leadership frontrunner has already appointed Douglas Oakervee, a former HS2 chairman, to carry out his own review of the project’s scope and costs, ahead of a decision in December.

The FT has been told that costs are spiralling because of a “poor ground conditions found during the surveying work” and plans for trains to “run at even higher speeds than other comparable rail projects”.

Allan Cook, brought in to take control after the departure of previous chairman Sir Terry Morgan, has written to Bernadette Kelly, the DfT’s permanent secretary, to make the warning, the paper said.

Construction has already been delayed until the end of the year, prompting contractor Balfour Beatty to warn that it would have to lay off staff if work was put on hold any longer.

Last week, HS2 announced it had abandoned its initial hunt for a contractor to build its station at Birmingham, after companies were unwilling to take on the risks associated with the £435m projected cost.

HS2 said it will rethink the procurement process for its Curzon Street station in order to reduce contractor risk and increase competition.

An HS2 spokesperson said: “We don't comment on leaks or speculation.

“We have previously noted that our chair, as you would expect, continues to scrutinise the programme, and regularly reports back to the department [for transport].

“We are determined to deliver a railway that rebalances the economy, creates jobs, boosts economic growth and is value for money for taxpayers.”

Asked about the future of HS2 at a leadership hustings last month, Mr Johnson replied: “It is going to cause a great deal of difficulties for my constituency.

“I think there are questions, legitimate questions, that any incoming prime minister would want to satisfy himself about, herself about, before what I think is a go or no-go decision in December about profiling of the spend and so on.”

The DfT said in a statement that Mr Cook would provide his final analysis “in due course”.