Rethinking High Speed 2, published today by the House of Lords economic affairs committee, said it was “far from convinced” the new high-speed railway will be built within the £55.7 billion budget and has called for a “major rethink” of the project.

The committee said the scheme had put too much emphasis on cutting journey times and not enough on the economic impact on regions. It said the first phase of the project, which will run between London and Birmingham, offered “little benefit” to northern cities, despite them being in most need of better rail infrastructure.

And it said the second phase, which would improve journey times between Leeds and Sheffield, risked never going ahead because of spending overruns.

Lord Forsyth of Drumlean, chairman of the economic affairs committee, said: “Commuter services in the north of England are badly overcrowded and reliant on ageing trains. Rail connections between northern cities are poor. As the committee suggested in its 2015 report, rail infrastructure in the north should be the government’s priority for investment, rather than improving north-south links which are already good. The north is being short-changed by the government’s present plans, especially as construction on HS2 is starting in the south. Any overcrowding relief from HS2 will mainly benefit London commuters.

“The plans for Northern Powerhouse Rail should be integrated with the plans for the northern section of HS2, and funding for the project ringfenced. This will allow rail investment in the north to be prioritised where it is most needed.

“The costs of HS2 do not appear to be under control. It is surprising therefore that the Government has not carried out a proper assessment of proposals to reduce the cost of HS2—such as lowering the speed of the railway or terminating in west London rather than Euston—which the Committee recommended in 2015. A new appraisal of the project is required.

“If costs overrun on the first phase of the project, there could be insufficient funding for the rest of the new railway. The northern sections of High Speed 2 must not be sacrificed to make up for overspending on the railway’s southern sections.”

A Department for Transport spokeswoman said: “By 2020, the government will have invested a record £13bn in transport across the North, and we have a clear plan for linking the Midlands and the North through HS2 and Northern Powerhouse Rail - the full benefits of which can only be delivered on the back of HS2.

“This is not either/or, we are clear we want both.

“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.”