An audience of about 100 people gathered at the Science and Industry Museum in Manchester to listen to Mr Johnson's speech.

The prime minister set out the four "ingredients" for the success of the UK as liveability, connectivity, culture, and power and responsibility.

He said this meant areas having great public services, enough affordable homes, safe streets, fast broadband, and more responsibility and accountability for local areas.

He added: "We are going to give greater powers to council leaders and communities.

"We are going to level up the powers offered to mayors so more people can benefit from the kind of local structures seen in London and here in Manchester."

Mr Johnson said young people growing up "a few miles away" from the centre of Manchester had felt "hopelessness, or the hope that one day they will get out and never come back".

"The crucial point is it certainly isn't really the fault of the places, and certainly isn't the fault of the people growing up there," he said.

"They haven't failed. It's we, us, the politicians, our politics has failed them."

The Northern Powerhouse rail project was part of Mr Johnson's wider commitment to deliver a high-speed railway link across the north of England, which would cost about £39bn.

Mr Burnham said what he heard from the prime minister "certainly sounded good" but warned he heard "something very similar in almost the same spot from [then Chancellor] George Osborne five years ago and, in those five years, rail services here have gone in reverse".

The mayor added: "The focus on buses too and a London-style transport system for Greater Manchester sounded very good to me but we will have to see real action now to back up the prime minister's words.

"What about Liverpool, Sheffield, Newcastle? All of those places need a commitment.

"Commuting is a daily nightmare for people in large parts of the North - it costs £4 here for a single bus journey, £1.50 in London. How can that be right?"

National Infrastructure Commission chairman Sir John Armitt said: "The PM's decision today must be integrated with plans for HS2, and matched with devolved funding and powers for city leaders in the North - as set out in our National Infrastructure Assessment."

Mr Johnson wore a badge saying "Northern Powerhouse" during the speech.

Labour's shadow transport secretary Mr McDonald said the plans had been "announced time and time again by the Conservatives".

He added: "With Boris Johnson's staggering failure to build a bridge across the Thames and an estuary airport I'm not confident he'll be able to deliver better train services between Leeds and Manchester.

"What we really need is Labour's Crossrail for the North, from Liverpool to Hull and up to the North East to unleash the economic potential of the region.

"Just upgrading the rail between Leeds and Manchester - the same distance as the Central Line on the London Underground - won't achieve that."

Mr Johnson used the speech to state he is committed to "rebalance power, growth and productivity across the UK".

He also said "the unglamorous local services which people use every day" - such as buses - needed improving.

A survey by the Northern Powerhouse Partnership (NPP) found companies believed the upgraded network would boost productivity and investment.

NPP director Henri Murison said: "This is a seminal moment for the North - the entire Northern Powerhouse concept is all about connecting the cities and towns of the north to boost productivity."

Leeds City Council leader Judith Blake said: "Northern Powerhouse Rail is key to our vision for a modern, reliable transport network that delivers faster journey times, additional capacity and greater reliability and I hope the government will now work with us to accelerate delivery of this project."

Source: BBC