A group of city mayors and council leaders representing more than 15 million people in the north of England are launching a campaign for the region to have its own specific budget, as a way of spreading economic growth further around the country.

The 19 politicians, who are board members of Transport for the North (TfN), have urged the creation of a so-called northern budget, combining £7bn in spending on immediate transport infrastructure pledges and significantly more in the coming years.

The plan was backed by Labour, with the shadow chancellor, John McDonnell, saying he would introduce the idea if the party came to power.

TfN argues that the money, including £39bn to construct the planned Northern Powerhouse rail network by 2040, is the bare minimum needed to catch up from decades of under-investment compared with London and the south-east.

The politicians also argue that it is particularly timely given Boris Johnson has called for significant infrastructure spending across the UK as a means of better spreading wealth.

In a separate announcement, the junior Treasury minister Simon Clarke is scheduled to visit several places in Greater Manchester on Thursday at the start of what is billed as a nationwide tour to pledge support for “left-behind areas”.

Clarke, who is to visit projects paid for by the government’s Stronger Towns fund, said he would “discuss with local leaders how the Treasury has placed support for the Northern Powerhouse project as one of its core objectives, backed up in recent weeks through the focus on transport, crime and health investment across the North”.

The TfN campaign calls for a significant increase in spending on transport infrastructure, primarily on road and rail links. The organisation’s board comprises a cross-party group including the metro mayor of Liverpool city region, Steve Rotheram, his Greater Manchester counterpart, Andy Burnham, the mayor of Sheffield city region, Dan Jarvis, the Tees Valley mayor, Ben Houchen, and the council leaders of cities including Leeds, Newcastle upon Tyne and York.

They are seeking more devolution on infrastructure matters and funding for a series of short- and long-term projects, including £7bn for a string of immediate road and rail projects.

McDonnell said: “This is exactly what’s needed and what Labour in government will deliver. We have had enough publicity stunts – we will secure a government of the north, for the north and by the north.”

Barry White, TfN’s chief executive, said: “These are the minimum requirements needed to overturn the underinvestment, under different governments, stretching back decades.

“While the government is planning for a one-year spending round for its departments against a Brexit backdrop, there is no reason why we can’t see real commitment and recognition of the ambitious pipeline of infrastructure investments the north so badly needs.”

Rotheram said: “Government may look different, but our asks are not. We’re consistent and focused in our plan for what infrastructure the north needs to unlock its full potential, not just for its own benefit, but for the whole UK. A northern budget would be the ultimate demonstration of that commitment.”

Clarke, whose official Treasury title is exchequer secretary, is to meet Burnham and visit a new cycling route in Astley, Wigan, part of Greater Manchester’s Bee Network bike and walking network.

He said: “The prime minister was clear that we want to see success spread across not just our big cities but our towns and rural areas – and it is our priority to support regional growth and prosperity to maximise the potential of places like Bolton, Farnworth and Astley as we leave the EU.”