Boris Johnson has staked his political reputation on delivering a “new anatomy of British transport” that will boost capacity and cut fares and journey times, as Downing Street seized control of the HS2 project and promised massive new spending on infrastructure.

Brushing off the objections of Tory MPs who warned him that the rail scheme would become an albatross around the government’s neck, the prime minister announced on Tuesday that work on laying the track could start as soon as April.

He claimed the line was essential as the “spine” of a new transport network to address what he called “the great musculoskeletal problem of UK transport”, and he compared objectors to sceptics about the M25 motorway around London.

Alongside the go-ahead for HS2, he confirmed that the government would spend £5bn over the next five years on bus and cycling infrastructure.

Johnson claimed his government was paving the way for a future “where high-speed trains glide between our great cities, where electric buses convey us cleanly around our towns, where self-driving cars roam along roads that are free of the congestion that causes so much pollution, and where a new generations of cyclists pedal safely and happily to school and work in tree-dappled sunlight on their own network of fully segregated cycle paths.”

The Green MP Caroline Lucas challenged Johnson over the claimed environmental benefits of the scheme, and he said it would prompt a shift to rail from other, more polluting forms of transport. “HS2 is the most low-carbon, efficient way of getting around this country,” Johnson said, adding mockingly: “Will nothing please them?”

Pressed by the shadow transport secretary, Andy McDonald, about whether tickets on the costly new rail network would be affordable, Johnson said: “The whole point of putting in another 200,000 seats in capacity is that it thereby drives down prices for the consumer. It is about competition.”

He was fiercely critical of the management of the much-delayed project, saying the company involved, HS2 Ltd, had “not made the task easier” and the costs had “exploded”. He announced a series of changes to the project’s governance, including appointing a minister to be directly responsible for its delivery, to avoid “further blowouts”.

HS2’s growing price tag had led Johnson to request a review of the scheme last summer. Douglas Oakervee’s assessment, published on Tuesday, strongly advised against cancelling the scheme, although it had many caveats on how to proceed, such as reducing the proposed number of trains an hour from 18 to 14 and reducing HS2 Ltd’s role.

Oakervee said the original rationale – a need for additional, reliable railway capacity – still held and there were no available alternatives. Upgrading existing lines would come at a high cost, including massive disruption for passengers, while cancellation would have “serious consequences for the supply chain, the fragile UK construction industry and confidence in UK infrastructure planning.”

HS2 Ltd will lose responsibility for redeveloping Euston station, which will be undertaken as a separate project, meaning high-speed trains to London are likely to terminate at Old Oak Common to the west for some years.

A new body may be set up to deliver the building of phase 2B – from Crewe to Manchester and the West Midlands to Leeds – along with Northern Powerhouse Rail, under the umbrella label of High Speed North.

Johnson said the train line would go ahead in its entirety, eliminating uncertainty about its route, but there would be a review as it was “right that we interrogate the methods and the costs as we go forward”.

The reaction from Conservative MPs – even those who had been sceptical about the project – was relatively muted, though Andrew Bridgen, the MP for North West Leicestershire, said HS2 would be an “albatross round the neck” of the government and branded it “unloved, unwanted and grossly mismanaged”.

Environmental groups were also disappointed. John Sauven, the Greenpeace director, said it gave Johnson the “dubious honour of being this century’s largest destroyer of ancient woodlands in the UK”.

No 10 will be worried that amid such fanfare and promises of bringing new infrastructure to the north of England, passengers in Manchester and Leeds will be dispirited to learn that HS2 is not forecast to be delivered to them until somewhere between 2037 and 2040.

Johnson’s team hope to compress this timetable, in part by integrating this final phase of the project into work on existing and new transport routes, such as a planned higher-speed rail link between Manchester and Leeds.

Details of this remain vague but the government is committed to publishing the outline of an HS2 integration plan by the end of the week.

Andy Burnham, the mayor of Greater Manchester, said he welcomed the headline commitment to HS2 but warned that there was “a lot of detail lacking” on what would happen in the north.

“The prime minister has today listened and gone a considerable distance towards the case I made at the weekend for a new, integrated east-west and north-south railway for the north of England. That is why I welcome what he has announced today.”

But he asked the government to set a firm timetable for Northern Powerhouse Rail, as well as the northern HS2 spurs to Leeds and Manchester. He also demanded urgent upgrades to the existing railway, which he said “ruins journeys on a daily basis”.