Labour’s leadership is under pressure this weekend to reconsider its support for the £56bn HS2 high-speed rail link, as concern grows among northern MPs that the plan fails to address their areas’ economic needs.

Several senior Labour MPs have told the Observer that the huge sum of money earmarked for the project, which will connect London to Leeds and Manchester via Birmingham in the first and second phases, would be better spent on connecting northern cities to one another.

They argue that other schemes such as Northern Powerhouse Rail (otherwise knows as HS3 or Crossrail for the North) – a project that would create a high-speed link between Liverpool, Manchester, Sheffield, Leeds, York and Hull – would deliver far greater economic benefits and be far cheaper. It would also, as a result, free up funds for Labour to spend on other infrastructure and investment schemes.

Lisa Nandy, the Labour MP for Wigan, said: “It’s becoming increasingly difficult to argue in favour of HS2 in my constituency. Much more important to our region is Crossrail for the North, which would bring desperately needed improvements to east-west connectivity.”

Nandy said journey times between London and northern towns and cities were already short compared with those between northern centres. “The journey from Wigan to Newcastle takes three and a half hours, without accounting for frequent delays and cancellations. From Wigan to London, which is a longer distance, it takes two hours.”

Facebook Twitter Pinterest Lisa Nandy, MP for Wigan. Photograph: Sarah Lee/The Observer

Karl Turner, the shadow transport minister responsible for shipping, aviation and road safety, speaking in his capacity as MP for Hull East, said he thought that HS2 would cost a “phenomenal amount of money”.

“In terms of creating jobs and benefiting my constituents, building Crossrail for the North and investing in existing rail networks in the region offers a better deal,” Turner said.

So far around £4bn has been spent on HS2, on a combination of consultancy and legal costs, land acquisition and early construction work in London and Birmingham.

Labour’s Andy McDonald, the shadow transport secretary, said that the party was committed both to HS2 and to improving connectivity between other towns and cities in the north. But he made clear that there would be limits to what Labour would be prepared to pay.

“It’s essential that the phases of HS2 align with the much-needed upgrades to railways in the Midlands and the development of Crossrail for the NorthPhase two has particularly strong economic benefits, so clarity is urgently needed. The project’s doubters have raised their heads again recently. I say: it’s not a question of either-or. It is both. Having said that, there will be no blank cheque from Labour.”

While the government is determined to press ahead, despite many of its own MPs along the route being opposed, anti-HS2 lobbyists increasingly believe Labour might be open to rethinking its support, in part because of this concern over costs.

The New Economics Foundation (NEF), a Corbynite thinktank favoured by the shadow chancellor, John McDonnell, has long argued for HS2 to be scrapped in favour of alternative transport investment. It is due to publish a report on HS2 in the coming weeks, which is expected to raise new questions about whether it is good value for money. In 2013, the NEF said there was “little evidence” to back arguments in favour of HS2.

HS2 will slash journey times from London to Birmingham from 81 to 49 minutes, and from London to Manchester from 124 to 67 minutes. But opponents argue that this could put those cities into London’s commuter catchment area and suck more investment into the capital.

MPs in constituencies further north point out that the benefits are less, timewise, for their areas. The eastern leg of the track will only go as far Church Fenton, south of York, after which trains will continue to use existing rail lines. Ian Mearns, MP for Gateshead, said: “Twenty years ago, there was a train that travelled from Newcastle to London [along the east coast mainline] in 160 minutes. With HS2 we will be spending another £53bn 40 years later, and by going on that route people could gain just 20 minutes.” Mearns said that this showed HS2 was “little more than a vanity project”.

The government finally committed to building HS2 in 2012 with a £33bn budget. The costs were revised upwards to £42.6bn in 2013 and then to £55.7bn in 2015. Some estimates have put the final cost of the project at more than £100bn.

Andy Burnham, the mayor of Greater Manchester, said in 2014 that HS2 represented a “poor deal for most of the region’s taxpayers”.

Jo Platt, MP for Leigh, said that HS2 would run through her constituency “without offering any connectivity”, while Emma Hardy, MP for Hull West, said that Crossrail for the North would “make a huge difference, while being far less disruptive than HS2”.

Meanwhile Sir Kevin Barron, the MP for Rother Valley, who has supported the project thus far, said that he was being forced to rethink because of plans to build the eastern leg of HS2 along the M18 motorway.

“It is the most senseless thing I’ve ever seen,” Barron said. “If it goes ahead as proposed, HS2 is going to disrupt the existing rail network from Sheffield to Doncaster. We were told HS2 was going to improve connectivity, capacity and create jobs, but it does none of that under these proposals. If they do not change I will vote against it.”