I’m not a war correspondent. But it’s 3am and, like every night this week, I’ve been woken by the sound of sirens outside, alarms on my phone and a calm voice-broadcast in the corridor of my hotel telling me to go to the basement. I scramble into some clothes and fumble my way down to the hotel laundry/bomb shelter. The smell of detergent is overpowering but also somehow reassuring. I take in the sleep-deprived faces of my fellow basement dwellers: a group of Spanish nuns; a couple of mysterious American “technology workers” with their local girlfriends; and the real-deal journalists and war correspondents who remain entirely calm and tell us: “This is nothing. You should have been in Afghanistan last year.”

Why am I here?

Like so many others I was appalled and angry when Vladimir Putin launched his unprovoked assault on Ukraine in 2022. Unlike any war I could remember, this one seemed morally straightforward: a country that wanted nothing more than the right to self-determination v a bullying neighbour who still saw the world through an imperial lens.

I wanted to do something to help. And, other than offer a little money, the only thing I could usefully do was make a documentary. I could help educate the world as to what was going on and perhaps change a few minds. Even back in 2022 I had heard the “contrarian” and “realist” voices suggesting that this was the US’s war, or Nato’s – that we had provoked Putin, who was only “defending his back yard”.

But what to make a film about? The biggest problem with activist film-making, I know from experience, is that it usually only reaches those who already agree with you. How do you reach an audience who wouldn’t normally watch a film about the geopolitics of Ukraine? That was when producer Lawrence Elman called me up and told me he had secured access to the Klitschko brothers.

Vitali and his younger brother Wladimir Klitschko were two of the most successful heavyweight boxers of all time. For more than a decade at the turn of the century, they dominated the sport and became Ukraine’s most famous export. Now, Vitali was the mayor of Kyiv and, after President Zelenskiy, perhaps the most potent politician in the country; he had adopted a pro-EU stance ever since the Orange revolution protests of 2004. This, of course, was the way to make a film with a wider reach: make a political film that felt like a sports film. So we set off to meet Vitali and Wladimir in November 2022. That was the start of almost two years of travelling back and forth on the night train from Poland to Kyiv, with my co-director Edgar Dubrovskiy and our Ukrainian co-producer Polina Borshchevska.

For almost a year it was hard to get below the surface with either of the brothers, but particularly with Vitali, the mayor. Although there was always a twinkle in his eye, a roguish charm about him, after decades as a professional sportsman and then a politician he was extremely media-savvy and cautious of being caught off guard. At 2.03 metres (6ft 8in) and built like Arnold Schwarzenegger, he visited endless buildings that had been destroyed by Russian missiles, comforted the victims and their families, met visiting politicians from around the world and travelled all over the country at night in the back of a car, seeming to exist on about two hours sleep. But we never got a real emotional connection.

It took a tragedy to change that. Late last summer in Kyiv, a woman and a young child were killed by a missile while trying to get into a bomb shelter that was locked. A media frenzy ensued. Vitali was blamed and vilified. He was devastated. Even Zelenskiy got involved, calling for Vitali’s resignation. Vitali defended himself. It brought to the surface a conflict that has been simmering for years between these two giants of Ukrainian politics, a conflict that now became central to our film. Suddenly we had drama and emotional access. His mother, his ex-wife and his children agreed to be filmed. Vitali began to take shape as that rarest of things: a dedicated and heroic leader.

A lot of Ukrainians won’t necessarily agree with me. They are, perhaps understandably, deeply cynical about their politicians. They have been betrayed, misled and disappointed repeatedly. Levels of trust are minimal, conspiracy theories abound. Spend enough time in Kyiv and you will hear that every single politician has mafia links and has bank accounts in the Virgin Islands stuffed with looted state funds.

We heard these accusations frequently against Vitali and felt deeply uneasy about them. Were we being duped? We tried to find the source of the rumours. We talked to political observers and investigative journalists. It became obvious that nobody had any actual evidence against the Klitschkos. The worst that could be levelled at him was that he had bad taste in architecture and had allowed construction companies to destroy old buildings in the city to make way for unattractive developments.

Set against this, I saw someone living an almost monastic life – exercising ferociously every day, getting by on a few hours of sleep, working as hard as he can for his city and his people. I am not sure you could ask for much more.

• Klitschko: More Than a Fight is on Sky Documentaries and Now from 15 August, with an Australia release to be confirmed