It is the last day of filming on Castles in the Sky. We are in Eddie Izzard’s trailer in a car park in Edinburgh. It is sparse – no home comforts here – with just an iPhone, a pair of headphones and a script on the table to hint that it is in use. “You’re from The Big Issue,” he says. “Oh, well that’s good. Not Nazis Weekly, then?”

Izzard wears the 1940s scientist chic well: braces, horn-rimmed glasses, slick side-parting. “I seem to morph quite easily into different looks,” he says with a lopsided grin. “This is a good one.”

But he is tired. Filming has been intense, a 90-minute drama filmed on a documentary budget. What a story though. Izzard plays Robert Watson-Watt, the scientist from Brechin whose team developed radar – beating the German scientists to this game-changing invention, enabling the early detection of bombing raids and victory in the Battle of Britain.

I’m somewhat encyclopaedic about World War Two

“It’s a good role and a great story,” says Izzard. “I knew about radar and I’m somewhat encyclopaedic about World War Two but I didn’t know it was Robert Watson-Watt who put it together.

“It is good to get their story out to people. It is a kind of Rocky for scientists; a story of these people pulling off this incredible invention on a wing and a prayer. I’m interested in all history, not just this period. But World War Two is incredible because of the energy changes in the world.

“That is why wars get into our focus. A lot of things are changing at once. Times of extremes are very interesting.”

But war stories are just one of Izzard’s interests. An obsessive and an enthusiast, his mind jumps from one subject to another at an alarming pace. This will surprise no one who has witnessed his stand-up.

A schedule that includes appearing in almost every scene of this film, preparing for stand-up shows in German, French and English, preparing for a pilot season in the US and shooting the TV series Hannibal in Canada is extreme by any standards.

But Izzard is also plotting to run for political office. Already a strong presence in the Labour Party, the comic has promised to stand in the “personality-led” race for London mayor, though Tessa Jowell is Labour’s top candidate for 2016. And if his bid to be mayor doesn’t succeed?

He has another plan…

Do you feel at home in Edinburgh after so many festival appearances? I did 12 Edinburgh Festivals and had about five or six that were not good. They are good to look back on but were really tough. Then after six bad ones I did four good ones and two that were in the middle. But I’m a tenacious bastard, that is one of my things.

Some people are really determined but are also really evil

Is that a characteristic you admire in people? As long as they have a heart. Some people are really determined but are also really evil. So determination and struggle and doing good and interesting work – I admire those people. Nelson Mandela is obviously one. He may have been one of the greatest people who has ever lived. Because he’s not calling on God, he’s not saying he is a saint, he is just a guy but he did push very hard and did it with such honour. He learnt Afrikaans, he learnt the language of people who were against him. I’m learning languages and doing stand up in the languages of people who are not against us but who in our history we have been pitted against. I’m doing stand-up in German.

How do you make your comedy universal to work across different languages and cultures? I’ve made my comedy universal for about 15 years now. It is only the cultural references that are different. There are mainstream audiences and alternative audiences in every country. I’m okay as long as I don’t get in front of a mainstream one because they’ll never get me. But an alternative audience just need to hear the words. Same stuff, change the language. It is the right way to follow this film. After playing the man who helped get the Nazi disease and cancer out of Germany, I’ll go and do stand-up, as me, in that country. Since 1945 they have tried to be an exemplary country. It is only the Nazis that tried to kidnap the country. And they are never going back in that direction. So this whole thing about whether America bugged Angela Merkel’s phone – I just think what is the point? What bad stuff is going to come up? What are you listening for? I don’t see Obama doing it – I presume someone left the gas on from the Bush era. They should be bugging people who are trying to do America harm, not a democratic European country. It doesn’t make any sense.

You’re increasingly vocal about politics and have a higher profile in the Labour Party than most MPs. You’ve spoken out against Scottish Independence and the monarchy and in favour of the EU, so will you run for office as you’ve promised? That is still very much on for 2020. I’ll be doing that.

Will that be as Labour candidate or London mayor? It could be standing as an MP if there is someone else [from Labour] in the job as London mayor. But yes, I’ll either be standing for parliament or for mayor by then.

Before then, what are your acting ambitions? Being good in better roles. Onwards and upwards. Stuff outside the comfort zone. Keep pushing it. My early stuff is not great – I had to hit brick walls before finding my feet. But I have my feet under the table now. When did I realise I knew what I was doing? Good question: I saw something towards the end of shooting Lost Christmas [in 2011] that’s stayed with me. It was subtle, sucking the camera in rather than blowing the information into the camera.

How important was your new character’s role in the war effort? Robert Watson-Watt was tenacious as hell. I’ll always play characters who are determined bastards. Without him and his team the Germans could’ve invaded and occupied Britain. If that had happened it would’ve been much more difficult to get the Nazi cancer out of Germany. They were expecting every day, right through the summer of 1940, that the invasion would come. Without the invention of radar the result of the war could have been very different – exactly how different is impossible to tell. It builds up to the Battle of Britain, and the big question is whether we will have a system that can give us 20 minutes to get our planes up there rather than chasing after their planes when they have already bombed the crap out of us.

He is backed by Churchill [played by Tim McInnerny]. This is Churchill during his wilderness years. He is not in power, he is a backbencher, but is pointing out that Hitler might be a danger. He is rising back up after being out of favour for some time. It isn’t that Watson-Watt backed the right horse in Churchill, it is that Churchill backed the right horse in Watson-Watt.

While he saves the country, it destroys his marriage

It’s a nice change to see a war story where the scientist is the hero. Barnes Wallis is known for inventing the bouncing bomb and RJ Mitchell is known for building the Spitfire. But Spitfires are beautiful to look at – you can show dogfights – and in Wallis’ story you can show the endless bouncing bomb trials. But with radar, it is difficult to grab the visuals on it. So we go through the story of the gang trying to make it happen and Watson-Watt’s family life. Laura Fraser and I filmed the entire 24 years of Watson-Watt’s relationship with his wife over three days with emotions going from positive to negative. It was tricky. While he saves the country, it destroys his marriage.

Are you a science boffin as well as a linguist? I did sciences up to university, so this does cross over into areas I know. I don’t think I would have done it but you rewind your life and think, why didn’t I concentrate more? I could have studied physics. There was a point when I was really digging physics and now I can dig it even more. In this film it is mission stuff, and when there is a real mission you can get into it. They began by trying to copy the rumoured Nazi death rays and came up with something different. It sounds very science fiction but this is applied science, science that makes things happen. You know exactly what they are trying to do with radar – save the country.

There have been some great war films – what are your favourites? One that was very interesting was Ike: Countdown to D-Day, which has Tom Selleck playing Eisenhower. That’s an interesting one not many people know about [he finds a picture on his phone]. He looks great, doesn’t he? Hope and Glory is another good one about being evacuated, like my dad was at that time. I grew up with my dad’s stories about how he could see London burning from St Albans.

Where do you go from here? I am in the middle of a massive tour, I’m heading off to do Hannibal, I want to work in as many countries as I can. I also have to write my own films. I’m working on several, which is exciting. I need to get those out of my head…

Castles in the Sky is on BBC Two at 9pm on September 4

Eddie Izzard

Eddie Izzard: “Times of extremes are very interesting”