Almost exactly a year ago, Chris Boardman – the Olympic champion turned walking and cycling commissioner – unveiled a bold vision: Greater Manchester was to turn itself into a Dutch-style cycling paradise by building a 1,000-mile network of walking and biking routes called Beelines, after Manchester’s civic symbol, the worker bee.

A year on, the scheme has changed its name to the Bee Network after a rather embarrassing copyright infringement, and has expanded to cover 1,800 miles. Yet so far, work has only begun on one tiny section – a bit of towpath in Wigan known as the “muddy mile” – and the first wodge of money has already gone.

Boardman said from the start that it would cost £1.5bn to build the network. This is not much, he will tell you, pointing out the government has agreed to spend £1.4bn upgrading a roundabout near Bedford and building a new 10-mile dual carriageway. That is £1.4bn on a project engineers boast could save drivers a whole 10 minutes.

So far, Boardman has been given £160m – a brave move by Greater Manchester’s mayor, Andy Burnham, who was under pressure to spend it on roads instead, but far short of the full amount.

That sum is now allocated, according to a report to be discussed by Greater Manchester combined authority on Friday. Over the past year, the 10 constituent councils have been submitting bids for the cash to pay for their parts of the Bee Network. More than 50 schemes have been granted “programme entry” so far, including a jazzy cycle bridge from Stockport railway station to the town centre and the creation of a “mini Holland” in a residential neighbourhood in Levenshulme.

A visualisation of Ashton-under-Lyne town centre in Tameside if it is revamped to become part of Greater Manchester’s Bee Network. Photograph: TfGM

Assuming the GMCA approves the latest tranche of Bee Network schemes – which includes an “active neighbourhood” in Urmston, Trafford, a revamp of Ashton-under-Lyne town centre in Tameside and links to the new RHS garden in Salford – the £160m pot will already have been overspent by £74m.

So where is the money going to come from? No one seems sure. Speaking on Monday at the launch of Our Network, Burnham’s vision for an integrated transport system, Boardman reiterated the full £1.5bn cost.

He hopes the government will listen to a plea he made last week to consider the negative effect car-centric planning has on the environment and people’s health. In a letter to the transport secretary, Chris Grayling, he argued current economic appraisal models used by the Treasury to decide whether to fund a new motorway or a segregated cycle lane “do not take full account of the negative consequences of making private car use easier, nor do they take full account of the benefits of walking and cycling on our health, wellbeing and environment”.

Burnham seemed to agree, saying on Monday: “Ask yourself this: which form of transport investment delivers the most benefit? Build roads and you may get an economic benefit but not an environmental benefit. If you invest in Metrolink, you deliver economic and environmental benefits. But if you invest in a walking and cycling network, you get economic and environmental but also health benefits.”

Why then, you might ask, is Burnham exempting private cars from his forthcoming clean-air charges? He says it is because the levies would punish the least wealthy drivers in society, who cannot afford to upgrade to cleaner vehicles.

But driving is already the preserve of the rich, with the most disadvantaged people disproportionately likely to live near the busiest roads with the dirtiest air. In south Manchester, one primary school cannot open its windows because the air is so polluted from the neighbouring Princess Road.

In 2016, the Royal College of Physicians estimated ambient air pollution causes 40,000 premature deaths a year in the UK, at an estimated social cost of £22bn per year. Adjusting these figures proportionally to account for population, this means there are 2,000 premature deaths in Greater Manchester per year, where child asthma rates are already twice the national average. Then there is the cost to businesses of congestion, estimated at £1.3bn a year.

“We have to stop building for cars,” said Burnham, as he plugged an as-yet-unfunded plan to bring the UK’s largest public bike-hire scheme to Greater Manchester next year.

It is all fine talk. But until the government starts to see investments in cycling and walking as more important than making car journeys 10 minutes quicker, we will continue to risk life and limb on unsafe roads, breathing filthy air.