A scrapped “emerald necklace” cycleway up the spine of the country alongside HS2 would have delivered a return on investment of up to five times greater than the rail project itself, an FoI request has revealed – but neither the government nor HS2 Ltd will fund it.

A 50-page report outlining the business case for the national cycleway, obtained by the Guardian, reveals health, congestion and economic benefits of between £3 and £8 per £1 spent. The return on investment of HS2 itself, meanwhile, is just £1.5-£1.7 per £1, according to the National Audit Office. Campaigners say completing the cycleway should have been a “no-brainer”.

Last year, the government-owned HS2 Ltd was accused of watering down its legally binding commitments to “cycleproof” the rail route, by not providing capacity on bridges and tunnels for cycling. About 11.7 million people would live within three miles, or 15 minutes’ ride, of the cycleway running from London to Manchester, Liverpool and Leeds, via Birmingham, and building it would cost the equivalent of between £3.45 and £8.69 for each of these people.

The London Cycling Campaign’s Simon Munk said: “There is loads of evidence (including from the DfT itself) that cycling schemes offer better value for money than any other transport spending. Providing safe cycleways next to HS2 should have been a no-brainer. The cost would have been tiny comparatively.

“If the government want best value for money, and it really is a choice between HS2 and cycle tracks, they should have cut HS2. Of course, that’s ludicrous – the government could have done both.”

The vision, revealed as part of a feasibility study published last year, was to create a “legacy cycle network” linking communities in the HS2 corridor, within three miles of the new railway. It would build on the concept of the National Cycle Network, using lanes, canal towpaths, bridleways and disused railway lines, but with Dutch-quality standards.

Roger Geffen, Cycling UK’s policy director, said the biggest benefits would have been for local communities. “Sadly the HS2 cycleway train has left the platform. However, if there is one bit of this project that has shown exceptional value for money, it’s the local community links. It’s vital that these are retained so that HS2 helps people make local journeys by bike or foot, rather than severing them as currently planned.

“If the government wants local authorities to follow its forthcoming new cycling design guidance, it needs HS2 Ltd to set a good example – not a bad one,” he said.

The business case report, produced in 2014 by Phil Jones Associates (PJA) and Royal Haskoning, estimated demand for different parts of the proposed cycleway for leisure, utility and cycle-rail trips, and balanced those against the build costs. The report was not published with the feasibility study last year, however.

Analysing four indicative sections of cycleway, from busy urban routes to quieter rural and urban connecting paths, it found urban sections with multiple connections would see the highest returns of between £4.70 and £14.84 per £1 spent, considering both pessimistic and optimistic projections. For the quietest linear routes, returns could be between £1.54 and £5.53 per £1 spent.

Phil Jones, of PJA, said the cycleway’s high returns are “not surprising”, adding “cycling and walking schemes cost relatively little compared to major highways and railways, and create significant benefits, particularly in terms of public health”.

Benefits also include time savings, decongestion, absenteeism and collision and injury reductions.

Safe, attractive routes can also attract a broad demographic of people to cycling, including older people and children, women, ethnic minorities and disabled cyclists.

In its response to the FoI, the Department for Transport said “neither DfT nor HS2 Ltd have any plans to fund the national cycleway”.

A DfT spokesperson said: “HS2 will be the backbone of Britain’s rail network. The project is already delivering significant benefits to local people and economies, employing 7,000 people and 2,000 businesses.

“We would encourage local authorities interested in progressing cycle routes to incorporate them into Local Cycling and Walking Infrastructure plans [LCWIPs] and explore funding opportunities with their Local Enterprise Partnerships.”

There is currently no funding allocated to LCWIPs, however, which campaigners want to see change. The government is currently predicted to miss its own cycling target, achieving just a third of the 800m hoped-for extra cycling trips by 2025, with much of that predicted growth restricted to London.

HS2 Ltd did not respond to a request for comment.