The government has published ambitious proposals to build a national cycleway up the spine of England, creating “an emerald necklace of linear parks and paths” along the route of the HS2 railway.

Approximately 7 million people would live within a 10-minute bike ride of the national cycleway within the HS2 corridor, and an extra 2 million would be included were the cycle route to extend across the Pennines, where the government wants to build a new line known as Northern Powerhouse Rail.

The feasibility study was completed in 2016 but was only released by the government on Thursday. A covering note made clear that neither the Department for Transport nor HS2 Ltd, the company building the high-speed line, had any current plans to fund the national cycleway outlined in the study. Instead, councils would have to fund their own sections, with help from the private sector.

David Cameron commissioned the study when he was prime minister in 2013. He promised it would “kickstart a cycling revolution which would remove the barriers for a new generation of cyclists”.

The corridor considered by the study incorporates six of the largest cities in England, and more than 200 towns and villages, broadly following the route of HS2 between London, Birmingham, Leeds and Manchester. One person who took part in the consultation envisioned “an emerald necklace of linear parks and paths joining communities along the HS2 corridor”.

But John Grimshaw, an engineer who helped write the study, said not only had the government sat on the report for two years – a fact a DfT press officer put down to “extensive dialogue with local and national bodies” – but it had failed to tell HS2 to make sure the new bridges and tunnels crossing the rail line were safe and attractive for cyclists and walkers.

“HS2 hasn’t had instructions from government to include visionary new provision for walkers and cyclists. They are just designing for existing footpaths, even if that footpath is only used by one person a month,” he said.

Roger Geffen, of Cycling UK, said it was not too late for HS2 to take heed of the design principles laid down in the feasibility study. They say new cycle routes should offer complete continuity of route, with no barriers or signs telling cyclists to dismount, and with “careful” segregation from heavy traffic – plus no gradients over 5%.

“If they don’t get it right now, communities are going to be cut off from each other by HS2 and we will be stuck with the wrong bridges and tunnels for decades,” he said.

Chris Boardman, Greater Manchester’s cycling and walking commissioner, said it was a nice idea but he had reservations: “It’s disappointing that funding has not been set aside for this as part of the HS2 budget as it would deliver a host of environmental and health benefits. It would also go some way to connecting communities back together in instances where the new rail line will act as a severance.”