The costs of the High Speed 2 (HS2) rail project to connect London with the Midlands and the North of England “appear to be out of control,” according to a House of Lords report.

The first phase of HS2, linking London with Birmingham, has a budget of £56bn and is due to open in 2026.

The chair of the Economic Affairs Committee, Lord Forsyth of Drumlean, said: “If costs overrun on the first phase of the project, there could be insufficient funding for the rest of the new railway.”

In a new report, Rethinking High Speed 2, the committee says the priority for investment in the rail network should be the north of England.

The former chairman of HS2, Sir Terry Morgan, told the Committee that “nobody knows” what the final costs of the project will be.

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Launching the report, Lord Forsyth said: “Commuter services in the north of England are badly overcrowded and reliant on ageing trains. 

“Rail connections between northern cities are poor. 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.

“The northern sections of High Speed 2 must not be sacrificed to make up for overspending on the railway’s southern sections.”

Four years ago the committee urged the government to consider whether improving links in the north of England would be a better investment than HS2. It also recommended reducing the cost of HS2, such as lowering the speed of the railway or terminating in west London rather than Euston.

The committee includes two former chancellors of the Exchequer, a former cabinet secretary and former permanent secretaries to the Treasury and the Foreign Office.

Ahead of the report, the rail minister, Andrew Jones, told The Independent: “We will overcome some of the capacity problems with a variety of different measures. Digital signalling, longer trains and constructing new lines. And HS2 is a key part of that.”

Mr Jones is MP for Harrogate and Knaresborough, and chaired the Northern Electrification Taskforce.

“I took the HS2 bill through the house, I’m a big supporter of HS2 and I want to see it happen,” he said. “As it develops, I think people will realise it will make a step change for journeys around our country.”

There is growing political opposition to the high speed rail project. Potential Tory leaders including Boris Johnson, Esther McVey and Andrea Leadsom have all spoken out against HS2.