Britain should aim to increase cycling use more than tenfold in the next few decades by investing £1bn-plus a year to make its roads more cyclist-friendly, a cross-party report by MPs and peers recommends.

Such a scheme would pay for itself many times over, boosting the economy and health of the nation by reducing pollution, congestion and inactivity, according to the findings of the Get Britain Cycling inquiry by the all-party parliamentary cycling group.

The benefits would be so widespread that the strategy should be funded not just by the Department for Transport but health, education and business, it says.

The committee, which heard weeks of evidence from ministers, cycling experts and others, has presented the government with a list of recommendations, including a target for cycle use to rise from its current level of about 2% of all journeys to 10% by 2025 and 25% by 2050.

To finance this, spending on cycling projects should be boosted from around £2 a person a year, as at present in most of England, to £10 and then £20.

Above all, the country needs "a fundamental cultural shift in how we think about the way we travel", the committee's co-chairs, the Labour MP Ian Austin and his Liberal Democrat colleague Julian Huppert, say in an introduction. "Cycling needs to be not just a personal option, when we decide how to travel for work, school or leisure, but a core issue when planning our streets, roads, buildings and communities," they argue.

A key element would be a long-term commitment to redesign roads and other infrastructure to make them more cycle friendly, the report says, noting that changes such as segregated cycle lanes and improved junctions would also benefit drivers as well as pedestrians.

The committee is recommending a legal requirement for the needs of cyclists and pedestrians to be taken into account at the start of all development schemes, including for housing and business as well as roads, with the existing network revamped to make it less forbidding.

Other recommendations focus on safety – for example, the extension of urban 20mph speed limits, better lorry design and more stringent police action following serious incidents – and more cycle training, including at all schools.

The report stresses how achievable ambitious increases in bike use can be: Seville, in Spain, managed a tenfold rise in three years. But any such goals hinge on strong and consistent leadership from the top of government. This will be the key test for the inquiry, which heard an admission from Norman Baker, the junior transport minister responsible for cycling, that he had never once discussed his brief with David Cameron.

The government has promised a formal response to the report. Huppert said: "That's what we'll have to see. The onus is on the prime minister to show that he does have that vision."

The committee says there should be a cross-departmental plan for cycling, with a national "cycling champion" to ensure unified policy.

"If you see cycling as a sub-department of the Department for Transport and nothing else, no matter how good your cycling minister is they can't factor in the huge savings to public health of people cycling more, or the business growth, whether from a healthy workforce or this idea that people on bikes buy more than people in cars, because they can get to shops more easily," Huppert said. "It's not just about money and the way our roads are laid out, though those are critical, it's about that cross-department action."

Baker said his department was committed to getting people on bikes. He said: "We are grateful to the APPCG for raising the profile of cycling and we will respond to this report shortly. I am setting up a project team involving stakeholders and representatives from other Whitehall departments to set out how we would work together to get more people cycling."Cycling groups including the CTC and Sustrans welcomed the report. Jason Torrance, policy director of Sustrans, said: "We now need leadership from the heart of government and co-operation by every department to implement these recommendations in full, helping to create a healthier, happier, more prosperous nation."