The route of high-speed rail across the north of England has been unveiled, with the government stressing that the controversial project was "a vital engine for growth" that will benefit the whole nation from the moment the first trains run.

The second phase of the £33bn HS2 project, the Y-shaped network north of Birmingham to Manchester and Leeds, will include a new spur of high-speed track past Crewe, with an extra stop at Manchester airport on the main route – helping to bolster support in critical areas of the north as local residents fear the blight and noise construction will bring.

From 2033, the journey from Manchester to Birmingham should be cut to 41 minutes and from Manchester to London to 1hr 8min. The journey to Leeds will take 57 minutes from Birmingham, less than half the time it takes today.

However, the government has played down the speed and time savings to stress the need for extra capacity, along with the economic benefits and tens of thousands of jobs that the new infrastructure will bring. Department for Transport officials claim it will create at least 100,000 jobs.

Map - high spreed rail link route

Extending the high-speed track to Crewe will shorten journey times between London and Liverpool, where city leaders have feared falling further behind Manchester in investment. Train journeys to Scotland will also be much quicker. The stop at Manchester airport will help attract support from wealthy Cheshire residents with a fast and accessible route to the capital, muting potential protests of the kind seen across the Chilterns, where residents face the disruption of high-speed rail with none of the benefits.

On the eastern branch, Sheffield's promised South Yorkshire stop will be outside the city at Meadowhall – dismaying those hoping it would help revitalise the urban centre, as the transfer time may negate the benefits of the faster trains. A station on the M1 at Toton between Nottingham towards Derby will be the other stop on the eastern branch, as planners try to balance the demand for multiple stops with the extended journeys it would mean.

Leeds and Manchester will both have new terminals built alongside existing mainline stations in the city centres, at New Lane in the South bank area of Leeds and next to Piccadilly in Manchester.

Fresh controversy may be fuelled by deferring the Heathrow link, which was one element of HS2's logic.

The transport secretary, Patrick McLoughlin, said: "It isn't just for Manchester and Leeds – the north-west will get the benefits right away.

"We know it's going to upset a lot of people. We have got to take environmental considerations into account and make sure people are adequately compensated.

"As with previous consultations, we will work closely with communities and interested parties to find the right balance between delivering the essential infrastructure that we need and respecting the rights and justifiable concerns of those who will be most affected by HS2's construction. "

McLoughlin has agreed to bring forward the consultation dates and will ask his department to review the construction timetable to try to deliver HS2 to the north before 2033.

He said: "While doing nothing would be the easy choice it would also be the irresponsible choice. This is an unparalleled opportunity to secure a step-change in Britain's competitiveness and this government will do everything possible to ensure that the towns and cities in the Midlands and the north get the connections they need and deserve to thrive."

The chancellor, George Osborne, told the BBC that the economic benefits to all communities were "pretty compelling" but would not "come overnight" but said Britain had not undertaken enough of such big projects. He agreed it would be "very difficult" for households close to the proposed rail line, but said the government had chosen a route to cause "the minimum disruption".

The prime minister, David Cameron, said: "Linking communities and businesses across the country and shrinking the distances between our greatest cities, high-speed rail is an engine for growth that will help to drive regional regeneration and invigorate our regional economies.

"It is vital that we get on board the high-speed revolution. High-speed rail is a catalyst that will help to secure economic prosperity across Britain, rebalance our economy and support tens of thousands of jobs."

Business leaders and politicians in the north have been clamouring for the route. But economists are divided on whether the benefits will flow to the regions or boost London and the south-east more, based on studies from France and Spain.

A decision on building a high-speed link to Heathrow, originally destined to be part of the phase two announcement, has been deferred until the Davies commission on aviation capacity has reported after the next election.

HS2's opponents may seize on the delay, although the government said HS2 will immediately connect to Crossrail at a new Old Oak Common station in west London, speeding up links to the UK's main hub airport.

Labour backs HS2 but has said there were "worrying signs" the timetable for delivering it is slipping. The route is due to be finalised by the end of next year.

The first phase, from London to Birmingham, is planned to open in 2026.

Locations of the new stations (to be completed in 2032)

• Manchester – alongside the existing Piccadilly station

• Manchester airport – interchange by the M56 between Warburton Green and Davenport Green

• East Midlands – at Toton, between Nottingham and Derby and one mile from the M1

• Sheffield – at Meadowhall shopping centre

• Leeds – at New Lane in the South bank area connected to the main station by walkway.