A Labour government would rename the troubled high speed rail project as part of a major shake-up of the way it is managed – and scrap the company set up to manage the line.

The planned new service linking Birmingham with London, Leeds and Manchester would become the North-South Line. It is currently known as HS2, an abbreviation of High Speed Two.

And the business set up to manage the line, HS2 Ltd, would be ditched – with Network Rail taking over the management instead.

The planned change reflects concern about the ability of HS2 Ltd to manage the project and explain the benefits.

It also reflects Labour leader Ed Miliband’s belief that the new line, once complete, should remain in public ownership. Privatisation would be much easier if the service is managed by its own distinct business, as is currently the case.

Network Rail, which is responsible for existing rail infrastructure, would use engineers currently working on a major rail project in London called Crossrail to build the new line. While Crossrail trains will not start running until 2018, the bulk of the work will be completed by 2015, freeing up experienced staff to work on the high speed network.

The Shadow Transport Secretary, Maria Eagle, warned last week that Labour could withdraw support for the project if the cost exceeded £50 billion.

But party sources stress that this did not mean Labour was planning to end its support for the high speed network. Shadow ministers believe the project will be delivered within its current budget – which already includes a £16 billion contingency element to soak up any unexpected costs.

HS2 Ltd was originally set up by Lord Adonis, the former Labour transport secretary, while Gordon Brown was Prime Minister.

Despite increasing criticism of the planned new line, Labour believes it is essential because it is simply impossible to meet demand for rail travel on existing networks.

In particular, the West Coast Main Line, which is used for local and freight services as well as inter-city services, is running out of capacity. A study by Network Rail concluded that even if the West Coast Main Line was upgraded further – following a £9.9 billion upgrade programme completed in 2008 – there would be too few seats for passengers on long distance journeys, no room for much-needed freight services and the line would suffer years of disruption.

Birmingham City Council has warned that congestion on the West Coast Main Line could reach crisis point when a plans to run 16 major new freight services every day come into effect.

The new traffic will come from major new port on the north bank of the River Thames in Essex called the London Gateway which is currently under construction and expected to lead to a major increase in rail and road freight. Labour is concerned that HS2 Ltd has failed to explain why lack of capacity on existing lines makes a new rail network essential, and instead has allowed debate to focus on reduced journey times.

The commitment to building a new North-South line comes despite criticism from the Institute of Directors, which said the business case for the line linking London with Birmingham, Manchester and Leeds over the next 20 years “simply is not there”.

Simon Walker, the institute’s director general, said: “It is time for the Government to look at a thousand smaller projects instead of falling for one grand folly.”

Former Labour chancellor and transport secretary Alistair Darling has also withdrawn support for the project, warning of a potential “nightmare” for the rest of the network if the line drained cash from other rail schemes.

Free market think tank the Institute for Economic Affairs has claimed that the line could cost £80 billion.

Business leaders in Birmingham are firmly backing the project. Birmingham Chamber of Commerce described the £80 billion figure as “simply nonsense”.

A spokesman said: “The Institute of Economic Affairs in their criticism included a host of schemes that are nothing to do with HS2 and then bundled them together.”

Jerry Blackett, chief executive of Birmingham Chamber of Commerce Group, said: “We believe that the really ‘grand folly’ would be to believe that it is possible to squeeze meaningful amounts of capacity out of the existing rail network.

“Network Rail have made it very clear that this is not physically possible.