The Bourne franchise has made a name for itself with car chases, and The Bourne Ultimatum is no exception. At the climax of the third in the series, released later this month, Bourne is pursued through New York by a “black ops” assassin driving a VW Touareg. The 4x4, beloved of school run mums, becomes an instrument of mass destruction, ramming through busy intersections, stationary traffic and into the back of Damon’s stolen police car.

The tyre-smoking chase scene culminates in one of the biggest crashes in cinema history, a fact that Matt Damon might have reservations about. In real life, Damon anguishes over the damage automobiles are doing to the planet, even when they are driven sedately.

“I drive a Toyota Prius and I have one of the Lexus hybrids,” he says. “Next year I’m getting a Tesla Roadster, which I’m very, very excited about. It’s an electric car, gets about 250 miles to the charge and is fast as hell! I can’t wait to get it. Driving a green car is one of the ways we can all do a little more, so I’m trying to do that.”

Although Damon, not long married and with a baby daughter, says he makes a point of not getting caught up in the celebrity mania that comes with his job – “I’ve made a conscious effort to stay away from all that stuff. I don’t live in Los Angeles, so that helps” – his choice of car proves he is not immune to the Hollywood fashion for eco-friendly vehicles.

But it wasn’t always that way. Back in the early days, Damon and Ben Affleck, with whom he wrote the Oscar-winning film Good Will Hunting, were Hollywood’s hottest bachelors. Damon dated Winona Ryder, Minnie Driver and Penelope Cruz, and Affleck was linked to Jennifer Lopez. It was a dream come true for the pair who had grown up together in Boston, where they would cruise the streets looking for adventure.

“Ben had a big black 1969 Cadillac we called the Batmobile,” he remembers. “It was huge and had dark tinted windows and you’d start it up and it would go ‘glug, glug, glug’. It probably did five miles to the gallon, and we would drive around our home town in it. It could barely get down some streets – you had to start slowly turning the steering wheel well before you got to the corner. But cars like that are definitely in our past.”

Bourne may be Damon’s most famous character but it was the massive success of Good Will Hunting that catapulted him into the Hollywood superleague. He has since starred in films as diverse as Saving Private Ryan, The Talented Mr Ripley and as one of the all-star cast of Oceans Eleven and its two sequels. There is a sense, however, that he misses those early days when he was a penniless actor wandering the streets of Hollywood with nothing but a film script about a boy genius.

“Sometimes I wish I could go back to sleeping on the couch,” he says. “I think back to those days when I was sleeping on friends’ couches. For years I had two duffel bags and I went from set to set and everything I had in the world was in those two bags. I didn’t have a house. I had nothing. And I loved that and there was incredible freedom in it; I could be in and out of a place in a minute – I could have everything on my body and moving. And now I have 20 bags and cribs and strollers and Pack ’n Plays.”

It is not the only area where family life is in evidence. Audiences watching a stressed and haggard-looking Bourne as he races between Madrid, Moscow, Tangiers, Paris and New York may think that it is the result of some clever make-up or method acting on Damon’s part, but the reality, he says, is more domestic: he is simply showing the stress of fatherhood. He and his wife, Luciana Barroso, insisted their 14-month-old baby accompanied them on the film sets.

“Last night my daughter was up all night,” he says, rubbing his eyes. “My wife tries to help me when I’m working – she tries to do everything at night so I can rest, but the reality is that when you’re in a room with a baby who’s crying it doesn’t matter whether or not you’re the one who’s changing the diaper, you’re still going to be awake.

“Halfway through the movie Paul Greengrass [the director] looked at me and said, ‘You look terrible.’ I told him, ‘I’m sorry. I’m awake all night with the baby’, to which he said, ‘No, it’s really good. She came along just at the right time – she’s really helping your performance.’ In the previous two Bourne films I’d have to achieve that same ragged look by staying out all night in Paris.”

He is feeling his age in other ways, too. “I realised how little of a life I had on the first two Bourne movies because I guess I just used to work and then I’d go to the gym and then I’d go to sleep – maybe go out on the town. On this one I was in shape at the beginning of the filming and then I slowly got out of shape because I never had the time to work out. By the end of the movie my jacket was being zipped higher and higher.”

The stunt sequences have also taken their toll this time around. “On the first movie, Doug Liman [director of The Bourne Identity and executive producer of the latest film] and I had to put our heads together, because this role was so different for me. We tried to figure out what were the best ways to make me believable in the role, and one of the things we came up with was that I should do as many of the stunts as possible and that he shoots it in a way where it’s obviously me.

“That really worked well for us, so if it’s a fight scene it means I have to give up my weekend to go learn a fight and learn the choreography. The problem with that is that in the first movie I was 29 and in this latest one I’m 36, so I definitely felt my age. Particularly in the big fight scene in Tangiers, where Joey Ansah – the other actor I’m fighting – is 23. When the first [Bourne] movie came out he was probably still in high school. So I was like, ‘Oh, man, Joey, you’re killing me! You gotta slow down’.”

He says that in many ways it is a relief that the filming is over and he can repair to the family home in Miami for some R&R and await the delivery of his Tesla.

But he shouldn’t think that driving an electric car gets him off the eco-hook: in all, he and his entourage, including his family and minders, are estimated to have racked up more than 1m flying miles during the filming. “I feel bad about that,” confesses Damon. “I don’t take any trips that I don’t have to take, but for a movie like this we went all over Europe, back to New York and then back over to Europe.

“It was the hardest movie I’ve ever done in terms of scheduling. We had a 140-day schedule. The closest I’ve done before was 110 – there was a time when you could shoot a whole movie in 30 days. I was coming back from Europe a couple of months ago and I looked at my daughter’s passport: she was 11 months old at the time and she already had 11 stamps in her passport.”

That’s a record even Bourne himself might be proud of.

On his CD changer

Everything byU2– I’m a big fan. Also Moby and Elliott Smith. My wife is Argentinian and I’ve taken tango lessons, although I’m not very good at it, so I listen to Latin music too. I don’t want to generalise about my wife but I love being connected to that side to her