The business secretary, Vince Cable, has intervened in the debate over the controversial HS2 high-speed rail line by saying there is now a "compelling case" to speed up links to northern cities to help rebalance the British economy.

Ahead of the release of a landmark report on the £50bn project by its new chairman, Sir David Higgins, who delivered the 2012 London Olympics on time and on budget, Cable says the focus should be on creating jobs and prosperity outside the capital, and closing the north-south divide.

His remarks to the Observer reflect a growing awareness in government, and among project leaders that HS2 will happen only if it gains political and public support up and down the country and is not viewed primarily as a way of speeding up journeys in and out of London.

Under current plans, work on phase one of HS2, between London and Birmingham, is due to start in 2017, with the line, which will carry trains running at speeds of up to 225mph, opening for passengers in 2026. Work on phase two, the construction of lines from Birmingham to Manchester and Leeds, is not due to start until much later, with services not opening until 2032 or 2033.

Cable was speaking ahead of Wednesday's budget, when George Osborne will stress the need to sustain economic growth through investment and support for businesses "right across the country". The business secretary says he has been impressed by strong arguments put by northern council leaders, many of whom are demanding that phases one and two start at the same time if possible, to show this is a national scheme, not one aimed at boosting the south still further.

Cable, who is concerned by London's overheating property market, said: "Creating jobs outside London, and closing the gap between north and south, has been one of this government's top priorities. On every visit I make to the north of England, I've heard businesses and council leaders make a compelling case for getting to the north more quickly by accelerating parts of the HS2 build.

"That would ensure the economic benefits can be shared sooner by everyone around the country and deserves serious consideration by government."

Higgins will say in his 30-page report that the costs of HS2 can best be kept under control if there is a firm cross-party consensus behind building HS2, and if construction can be completed as soon as possible.

Sources close to HS2 say the new chairman will also "address the issues of rebalancing [the economy]" and will suggest that phase two be brought forward. "He will talk about the art of the possible and how the north can benefit as soon and as much as possible."

While the Conservatives and Liberal Democrats back HS2, Labour has qualified its support in recent months, saying there cannot be a "blank cheque" and that costs cannot rise above £50bn. Higgins is aware, say sources, of the need to lock in Labour backing with firm statements on cost control.

The appointment by ministers of Higgins, a no-nonsense Australian, is seen as a signal of government determination to press on with the project, despite resistance in many rural areas, including several Tory seats, through which the new lines will be built. Civic leaders in the north backed Cable. Nick Forbes, Labour leader of Newcastle city council, went even further, saying construction should begin in the north first. "Much of our rail network relies on Victorian engineering; modern high-speed rail links between the major northern cities would transform our economy by giving us significant aggregate benefits. Doing this as the first stage of HS2 would also signify serious intent by government to rebalance our economy, and send a strong message about the enormous growth potential of the north." The mayor of Liverpool, Joe Anderson, said: "If the aim is to rebalance the economy, we should get on with it in the north as soon as we can. We should start at both ends at the same time."

A new Opinium poll for the Observer found that just over a third of people (36%) back HS2, while 30% oppose it. By contrast 64% back improving existing connections between northern cities such as Liverpool, Manchester, Sheffield and Leeds – with just 4% opposed.

The problem with starting both HS2 phases at the same time, or in the north first, is that the current bill before parliament deals only with phase one, between London and Birmingham. Michael Byng, an expert on rail construction who has been working with Network Rail, said: "The really heavy costs of this are at the London end and if you do all that first you could end up with a perception issue of everybody saying, 'all this money's being spent within the M25'."

HS2 will cut journey time from London to Birmingham from one hour 21 minutes to 49 minutes. For London-Manchester it will fall from two hours eight minutes to one hour eight minutes, and for London-Leeds from two hours 12 minutes to one hour 23 minutes.