Former chancellor George Osborne - instigator of the Northern Powerhouse concept - said HS2 "must go ahead".
He also said the Government should go further and sign off HS3 - also known as Northern Powerhouse Rail - a fast rail route connecting cities in the North from east to west.
The London Evening Standard editor told BBC Radio 4's Today programme: "HS2 is absolutely critical to changing the economic geography of this country.
"For the nation that invented the railway, the fact we are the only nation in Europe without high-speed lines should be an embarrassment."
The former Conservative politician said the West Coast Main Line, connecting major cities such as London, Manchester, Liverpool and Glasgow, would be "completely packed" within the next three decades if capacity was not increased.
Mr Osborne added: "HS2 must go ahead. It must be accompanied by what is called Northern Powerhouse Rail or HS3, which is across the North. I think that's critical."
Appearing on the same programme, Andy Street, Mayor of the West Midlands, said: "The Prime Minister and the Government talk about 'levelling up', getting the Midlands, and indeed the North, to the sort of standards of wealth enjoyed in London.
"And I see this is an absolutely critical way of achieving that. And if it didn't go ahead, obviously it would set back our revival by decades."
Asked if he was worried HS2 could be ditched after Boris Johnson called for Cabinet ministers to review spending, Mr Street said: "Occasionally you have to just go through the cupboard and say which are the things that have perhaps gathered dust and need killing off. This is not in that category.
"This is literally a once-in-a-generation, game-changing investment. And I'm actually very confident that when the Government look in detail at the business case, they will see there is a good repayment on taxpayers' investment."
It comes after former Labour transport spokesman Lord Berkeley said Parliament was "seriously misled" over the costs of HS2, which would be poor value for money and bad for the environment.
He also accused the project of being "completely out of control financially".
But a HS2 Ltd spokesperson said there had been many individual views expressed about the HS2 project, of which Lord Berkeley's was just one.
Lord Berkeley's hard-hitting 70-page dissenting report into the high speed rail proposal listed several grave concerns.
Chief among them was the blow-out of estimated costs.
The network was initially expected to cost £50.1bn.
Latest estimates by HS2 Ltd, the private company in charge of the project, put the price at £88bn.
But Lord Berkeley says independent analysis arrives at a figure of at least £107.92bn.
Yesterday Tory backbencher Philip Davies urged the Chancellor to "pull the plug" on the HS2 rail project, branding it a "white elephant".
Mr Davies, MP for Shipley, called on ministers to "ensure the money is spent on infrastructure projects across the North to benefit the regional economy".
Speaking during Commons Treasury questions, Mr Davies said: "Now that Lord Berkeley has laid bare the overspend and lack of return on investment of HS2, will the Chancellor now pull the plug on this white elephant project and ensure the money is spent on infrastructure projects across the North to benefit the regional economy, starting with Northern Powerhouse rail, with a station stop in Bradford and the much needed and long awaited Shipley eastern bypass?"
Responding, Exchequer Secretary to the Treasury Simon Clarke replied: "I thank (him) for a characteristically robust Yorkshire question and as a fellow northern MP, I am obviously very keen to get cracking with higher transport infrastructure investment in the North.
"That is something which this Government is absolutely committed to do.
"On HS2 specifically as he knows the Government has commissioned the Oakervee Review to evaluate this scheme and this will report in due course. We will lay those findings before the Commons."