When I phoned the prime minister of Denmark, Anders Fogh Rasmussen, just before Christmas to ask if I could come for a run with him, I never really expected him to say yes. I knew that the 55-year-old had a history of running with the common folk - every day leading up to last year's Danish elections he invited different sectors of his electorate out for a jog. But I rather thought that once he had won, he would have better things to do with his time. I was wrong.

So it was that I found myself shivering in the icy drizzle outside Marienborg, Rasmussen's retreat north of Copenhagen, waiting for him to put on his trainers. I was nervous. His aide had told me his boss was on fighting form, having recently been downhill skiing with the prime minister of Slovenia. Not just that but, apparently, the former prime minister of Slovakia had managed the 7.5km cross-country route we were about to take just fine. National pride was at stake.

I was right to be worried.Rasmussen, a chiselled, Gillette man prototype with Pierce Brosnan eyes, is a machine, thanks to his insistence that his diary must allow an hour every day for sport - even if it means taking important calls from his kayak (Tony Blair thought he was at his desk until he heard the ripple of water and the tweet of birdsong), or gatecrashing the exercise sessions of other world leaders ("Mountain biking with George Bush at Camp David was rather special," he said). Rasmussen has been top dog in Denmark since 2001, and has made headlines for his unpleasantly tough immigration policy (though he assures me that Denmark is actually a fabulous place to be foreign - and I'm too out of puff to argue otherwise).

On our jaunt, we were tailed by just two bodyguards, one on foot and one on a bike that was dramatically abandoned when it got a puncture a kilometre in. The nonchalant response we received from ordinary Danes en route suggested that even these two were superfluous. When one woman asked the Guardian's photographer, stationed halfway around Lake Bagsvaerd, who he was waiting for, she looked very disappointed to be told it was only her prime minister.

I was pretty pleased when I spluttered to the end of the route, and even felt I had tested the prime minister a little. Then I made the mistake of asking him what important government business he had to attend to next. "Oh nothing," he said. "I am going to the gym."

Hear more from Helen Pidd and Prime Minister Rasmussen at theguardian.com/audio