The cost of HS2 should be slashed by limiting the speed of trains and making its London terminus Old Oak Common rather than Euston, according to a critical House of Lords report, which warns that better northern rail connections could be lost if the project blows its budget.

In a report that could stoke further doubts over high-speed rail after Conservative leadership candidates discussed axing the project, the Lords economic affairs committee said it was “far from convinced” that the £55.7bn price was credible, and the government should publish a new cost-benefit analysis.

The committee said the priority for new infrastructure should be the north. It called on the government to build new connections between cities from Liverpool across to Hull – the Northern Powerhouse Rail scheme – at the same time as the second phase of HS2, to guarantee their construction.

The committee chair, Lord Forsyth, said: “We’re aware that this project is not going to be completed within the government envelope of £56bn. The committee believes that there are very considerable benefits in the north from the proposals for east-west connectivity – so the funding for that should be ring-fenced..”

Forsyth said the committee, which includes the former chancellors Alistair Darling and Norman Lamont, did not want HS2 to be abandoned, but added: “There needs to be a new appraisal of the project … If you look at the data and assumptions of the business case, it’s pretty ancient and of doubtful quality.”

A report four years ago called on the Treasury to review the costs and examine potential savings. However, Forsyth said: “We assumed that the work would have been done as a matter of course – you’d expect these questions to be addressed and we were surprised that nothing had been done.”

The first phase of HS2 between London and Birmingham is due to be completed by 2026, with the high-speed railway eventually extending to Manchester and Leeds by 2033.

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Giving evidence, the former HS2 chairman Sir Terry Morgan – who also chaired Crossrail as it veered into delays and overspending – told the committee that the project could not be built to its current specification on budget. “I think the triangle of scope, cost and time – something has to give,” he said.

The report queried why the tracks were being built to accommodate speeds of up to 400km/h (250mph), when the top speed of the first batch of trains would be 360km/h – and differences in journey times at 300km/h are minimal. It also said billions could be saved by stopping services before central London, to change on to Crossrail at the planned Old Oak Common station.

The Department for Transport described the Lords report as a “thorough assessment of a complex project” but said it “fundamentally disagreed with parts of it”. A spokesperson said: “HS2 will deliver additional rail capacity, significantly improve connections and provide opportunities for economic growth – with around £92bn in benefits – for people and businesses across the north.”

According to HS2, more than 7,000 people are already either directly or indirectly employed on the project. A spokesperson said HS2 Ltd would consider the report’s recommendations: “We have strengthened our controls and are actively applying lessons learnt from recent infrastructure projects to ensure we have the most cost-effective approach.

“HS2 is fundamental to the delivery of Northern Powerhouse Rail. As regional leaders across the Midlands and north have repeatedly said, it’s not a case of either or, it’s both.”

Penny Gaines, the chair of Stop HS2, said: “Every independent report reaches the same conclusions, that HS2 is the wrong answer for the country’s transport needs.”