What can the UK learn from Copenhagen's 'Eiffel Tower' for burning rubbish?

I'm attempting to ski down a steep piste, it's like nothing I've ever experienced before.

Partly because it's a dry ski slope that feels more like sheet ice, so I'm struggling to stay in control, but mostly because I'm 80 metres above Copenhagen on the roof of a spectacular power plant, which turns the city's rubbish into heat and power for its residents.

I'm experiencing "hedonistic sustainability" - the idea that being environmentally conscious can also be fun and that you don't necessarily have to sacrifice pleasure to do things that are good for the planet.

It's a concept dreamed up by the architect behind this unique building, Bjarke Ingels.

The Amager Bakke waste energy plant dominates Copenhagen's skyline, a bold expression of the city's determination to forge ahead on climate action.

It's set to become the world's first carbon neutral city by 2025. A third of all Denmark's power comes from renewable sources.

In this Danish vision of a greener future, it seems power stations can be re-imagined: no longer dirty, ugly, polluting eyesores. As a fellow skier on the roof tells me: "It's a monument, like the Eiffel Tower, which is crazy because it's literally garbage!"

Every day 350 truck-loads of rubbish, which can't be recycled, are brought into the centre and burnt - heating water that's piped directly into 680,000 local homes, via a district heating system.

The smoke is purified, so no toxins are pumped out into the atmosphere. And down in the depths of the plant, groundbreaking carbon capture technology is being developed to remove all C02 from the emissions.

As the boss Jacob Simonsen tells me: "We are part of the city and we're proud to be a part of the solution.

"We actually receive a small amount of waste from the UK and you pay us to take it. Of course, we're happy to help you out, and also to receive your money, to make good, cheap and clean energy for the city of Copenhagen."

I want to find out whether the UK can learn from Copenhagen's approach. So I visit Denmark's Parliament to meet a politician who's helped push sustainability to the top of the agenda here. Ida Auken tells me: "I truly hope Copenhagen can inspire other cities."

Her message to Boris Johnson: "You need to do this right now. I fear that our kids are going to look at us and say, why did you not do anything? You knew it and you saw it and you did not act."

But Copenhagen's population, around 1.3 million, is only a fraction of the size of London's and Denmark's green image is far from perfect.

It's still Europe's biggest oil producer and one of the most heavily farmed countries in the world.

There are plenty of critics. I watched as Extinction Rebellion staged a surreal protest; dressed as frogs, birds, insects, even fungi, the group invaded Copenhagen's City Hall. Nine of them were arrested.

One of the organisers, Ida Dalsgaard Nicolaisen, told me: "It's a terrible lie that we are a green frontrunner. What we're good at in Denmark is making promises and making good stories about how sustainable we are.

"But we aren't really. We are one of the most polluting and emitting nations in the world per capita."

What Copenhagen is undeniably excellent at, though, is cycling. With bike paths, bike bridges, rental bikes everywhere - it's already regarded as the most cycle-friendly city in the world, but the authorities want to go even further.

By 2025 the goal is for 75% of all trips in the city to be by bike, on foot or public transport.

As I watch the busy school-run, with mums and dads happily pedaling their kids in on cargo bikes (most of them because it's simply more practical than using a car) it strikes me: Copenhagen has made it easy, enjoyable even, to live more sustainably.

Surely other cities can learn from that.

You can watch On Assignment on Tuesday October 26 at 10.45pm on ITV and afterwards on the ITV Hub.