Speaking at Labour’s economic conference in Liverpool, Mr McDonnell will set out plans for a “Barnett Formula for the North” - a reference to the mechanism for distributing government support for Scotland, Wales and Northern Ireland.
He will say that under current Conservative Government plans, London was set to receive twice the level of public investment per head than the North.
Labour would legislate to require ministers to audit their regional capital spend against economic need, he will say, and report to Parliament when the investment imbalances are “excessive”.
He is set to say: “We have to put an end to the Whitehall view that what’s good for the City of London is good for the country as a whole. It’s time for the rest of the country to get a look in.
“The Crossrail transport link alone is due to cost four times the entire public investment budget for Yorkshire, or six-and-a-half times that for the North East.
“We can’t, as a country, face the world after Brexit if we are not all able to pull together.
“We will make sure that no government can ever again bias its own investment plans so heavily against the majority of the country.”
A Conservative spokesman said: “Labour’s policy to borrow half a trillion pounds would crash our economy and threaten jobs and infrastructure.”