The success of New York's High Line park has reinvigorated our imagination in the way we use existing landscapes and architecture in our cities

Looking back on the story of New York's High Line in 20 years time, I wonder if we'll see it as having been the catalyst for a new era of design for our cities.

Having fallen in love with the structure of the old freight railway from the street, it was what High Line founder Robert Hammond saw when he got up on to the railway itself, that convinced him to try to save it. Here, running through the middle of Manhattan, was a mile and a half of wild flowers.

That was in 1999. Now, 12 years on, New York's park in the sky attracted more than 3.7 million visitors last year, has generated $2bn-worth of private investment (£1.3bn) surrounding the park and is predicted to exceed $900m (£562m) in new tax revenues for the city over the next 20 years.

Such figures are not to be sniffed at. For what started out as a rescue attempt by two neighbourhood residents (Hammond and Joshua David) with no design background, no plan and no money, has created the city's second most popular tourist attraction after the Museum of Modern Art. It is decisive evidence that it is increasingly the quality of our parks and public spaces, not the towering ambition of our skyline, that make our towns and cities stand out.

But it is what the High Line – and to a great extent London's Olympic Park – will make possible, that will define its legacy. By making a virtue of an industrial relic, the High Line offers a new, 21st-century experience of the city – not a sanctuary from it. In fact, the High Line offers views of the city that you'd get nowhere else. So, suddenly, in the middle of Manhattan, is a piece of infrastructure that is not only a green lung, but looks and smells beautiful; is a place that offers a new route to work, space for recreation and contemplation, and is regenerating an area. Once we have a park in the sky, the city is ours to re-imagine. Indeed, it must be re-imagined if we are to face the challenges we seem destined to face.

Which is why it so refreshing to see mainstream media, not long ago in thrall to Renzo Piano's Shard, filling pages with ideas for green cycleways in the sky, a new "Lido Line" offering a swimmable commuter route along Regent's Canal and an urban garden in the old Mail Rail tunnels (The Post Office Railway) beneath Oxford Street. All were the result of A High Line for London, a recent green infrastructure ideas competition that called for proposals that transcended the traditional idea of an urban park.

The winning idea, called "Pop Down" by Fletcher Priest Architects, proposed reinventing the disused tunnels of the Mail Rail that run for 10.5m as a public experience and urban mushroom farm. London with its history of hidden tunnels and lost rivers provided the inspiration for the idea, while the team tried to capitalise on the same sense of drama that the High Line creates by being in between the fabric of the city. In New York, there have also been plans to build a subterranean public space and in London a High Line in Tower Hamlets has also been proposed.

But unlocking the potential of forgotten spaces is often more easily achievable than reclaiming the architecture or infrastructure that creates them, as the saga of Battersea power station can attest. HTA Landscape Design's highly-commended idea "Bridge-it" proposed opening up inaccessible railway cuttings and sidings, and linking them together into green linear parks that connect existing London transport hubs and open spaces.

A much-celebrated project in East London is already showing what can be achieved by mapping the abandoned space in a neighbourhood and working with the local community to re-imagine it. Between 2009-10, J&L Gibbons and Muf architects delivered 10 projects as part of Making Space in Dalston. The Eastern Curve, once a overgrown and abandoned piece of railway land, was one of them. It is now a popular public space with trees to offer shade, warm weather cooling and improve air quality, and vegetable and herb growing areas for local people.

That a competition that would typically been considered niche has made it into the mainstream is extremely encouraging. It is in indicative of a groundswell of support for rethinking the conventional approach to designing public space and engaging with the sustainability agenda. That groundswell includes the Mayor of London's commitment to developing pocket parks; the US Embassy, which is behind a major green infrastructure development in Nine Elms; and private landowners such as Grosvenor, who was inspired by Cabe Space's Paved with Gold report to invest in the public realm.

In the wake of the Olympic Park's success, it's easy to forget how ambitious a project it was to transform 50 hectares of post-industrial wasteland in East London. More than 2m tonnes of soil was decontaminated and the largest wildflower meadow the UK has ever seen was planted.

While we are unlikely to see investment in public space on this scale again for a generation, as with community-led projects such as the High Line, if green infrastructure is designed and managed to a high quality, it can give credibility to wider regeneration issues. In straitened times, the creative reuse of our existing landscapes and their architecture, might be our only option.

Sue Illman is president of the Landscape Institute, which ran the High Line for London competition alongside the Garden Museum and the Mayor's Office. She is also founder of landscape architecture practice Illman Young Landscape Design