It's a challenge to pin down exactly what Gyles Brandreth actually does. He's been a fixture on daytime television for decades, had a five year spell in Parliament and boasts numerous writing credits: from novels to biographies. Yet he outright refuses to be confined to labels: “I describe what I do on the day that I do it. The nice thing for me is that I do lots of different things on lots of different days”.

It is a warm and breezy Monday morning and I'm at Hammersmith's Riverside Studios to chat about Brandreth's current project: being a playwright. In a few weeks he will be travelling north to the Edinburgh Fringe with a musical play he has co-written. It is called Wonderland and studies the relationship between the writer Lewis Carroll and an actress called Isa Bowman. Although Brandreth will not be part of the show's two-strong cast, to keep him on his toes he has a second production in town: The One To One Show. This consists of an hour of what Brandreth excels at: talking about himself.

For it is instantly clear as soon as we meet that nowhere is this man more home than in front of an audience. As soon as I switch on my video camera, he perks up and grins into the lens. He is a serial raconteur and delights in deftly slipping in an anecdote here and dropping a name there. Yet the garrulous persona masks a fiercely intelligent and highly motivated man.

Why did you want to write about this specific aspect of Lewis Carroll's life?

I wanted to write a musical version of Alice in Wonderland because I've been fascinated by the story all my life. Lewis Carroll was this complicated, fascinating man who was both an extraordinary writer, an academic, a mathematician, a clergyman, a teacher. We began to dig a little bit deeper and then we came across a book called 'Lewis Carroll By The Real Alice In Wonderland' which turned out to be an account of Lewis Carroll's life by a young actress called Isa Bowman. This is a play about a middle-aged academic and his intimate friendship he had with this young woman: an actress who was a teenager and then in her early twenties at the time of the play. We began to discover things we didn't know. What we have then ended up with is a play that somebody described as being a play, a musical, a box of tricks and a revelation, because it tells you things about Lewis Carroll that you didn't know before.

There are accusations levelled at Lewis Carroll that he had an unsavoury interest in children. What is your view?

Lewis Carroll was a famous distinguished photographer and he took a lot of photographs of young children. There has been no evidence at all of Lewis Carroll having an unhealthy interest in young children. There is literally no evidence of any kind. What we have unearthed is not a unhealthy interest in young children but actually quite a healthy interest in young actresses, but grown up actresses.

Under what conditions do you write?

I am a very disciplined writer. Mark Twain said the secret of success as a writer was application: you've got to apply the seat of the pants to the seat of the chair. That's the only way to get it done. So I get to my desk at eight in the morning and I leave it at seven in the evening and I just work away. I'm a work machine. This is because when I was small I remember being at the church service when I heard the reading from the book of proverbs: 'A little sleep, a little slumber, a little folding of the hand to rest, and poverty will come upon you like a vagabond and want like an armed man'. You don't work: you don't eat. I like to eat, so I work.

What are the challenges of writing a play?

One of the difficult things is that the stage directions are neither here nor there: it's all got to be done with dialogue. You've got to get the characters right. And also I've been working with a female – in the lovely shape of my composer and co-lyricist - it's been good for us. In a way also, writing the play we had the same sort of age difference between us as Lewis Carroll and Isa Bowman had. One of the interesting things about writing a play is that when you've finished it you have to give it away. So this play I wrote and gave it away to Iqbal Khan who is the director, flavour of the month, and an extraordinarily exciting new talent. I was recommended to him, if I may now name drop, by Harold Pinter and Simon Russell Beale. And they said this is the most intelligent man you will ever meet. He - like Lewis Carroll - was a mathematician and he found this extraordinary cast that we have.

Tell us about The One-To-One Show?

It is literally just me for an hour in the Pleasance Courtyard every afternoon at 4.30pm. And it's called The One-To-One Show because it's really stories – I hope funny stories – about interesting people that I've met one-to-one. There quite a lot about the theatre and language. I love language: it's power, it's what defines us, what differentiates us from the animals. As the philosopher says, 'no matter how eloquently the dog may bark, he cannot tell you that he parents were poor but honest'. It's also quite a lot about Politics, because I was an MP. I'm no longer an MP, I do want you to know that. It's a respectable show, I don't want you to be put off. When I was an MP I 'd like you to know that I dug my own moat.

Why do you write a diary?

I keep a diary to remind myself that I was there. I think it was Tallulah Bankhead who said 'Only good girls keep diaries, bad girls don't have the time'. It's a discipline. It reminds me of what I've done, it's a habit. I've been keeping a diary since I was about 11. If you don't keep a diary everything washes away. And you can live everything three times: you live it when you live it, you live it when you write it down, and you live it a third time when you re-read it'. Though I have to say rereading my diary for publication was a depressing experience. You shouldn't look back.

What do you like about the Edinburgh Festival?

I love it because at the one end you can go to a place like the Assembly Rooms and see a proper play with someone like Michael Maloney who stars in Brandreth's Wonderland. World class theatre. And then you can go down the royal mile and go into a laundrette and you find a lovely group called Lesbian Sweatshop presenting a musical version of Macbeth with marionettes. No other city in Europe is offering us that this Summer.

You saw the actor John Gielgud get booed in a performance of The Ides Of March in 1963. Have you ever received similar treatment?

I was very lucky to know Sir John Gielgud. On his ninetieth birthday he came and had lunch with me and my wife at the House of Commons and we said to him: “Oh Sir John we're so honoured that you should come and have lunch with us on your ninetieth birthday”. And he said: “My dears I'm delighted, you see all my real friends are dead”. He was a very amusing and delightful man. When I first came to Edinburgh and we did Zipp, a the end of the performance there was noise out there and the banging of seats and saw people standing up. And I thought “oh God they're leaving, it's been a disaster”. In fact they were standing up to cheer. Which if you've been a politician is a very unusual experience. So I find that if people stay through the show ungratified... I have been a member of parliament: I have been a politicians. I'm used to any kind of audience. When they get up and walk away I can cope, it's when they get up and start walking towards me that I get a little bit nervous.

What is the secret of networking and knowing lots of famous people?

Be not too proud to be there. One of the things with a diary is that actually you live much of your life for the diary. If in that room now was the Queen, Kylie Minogue, Jordan, Wayne Rooney you might... but I keep a diary, I'll go and see. So because I keep a diary I go out of my way. And I'm curious because I like to meet interesting people: because partly I suppose you hope some of their woofle dust will wash over you. Partly because it's just fascinating to see them. To see these people close to is fascinating: to find out how tiny some of the great film stars are, how huge Bill Clinton is. The most magical person I've met was curiously Desmond Tutu. Now you can read about that, you can see it on television, but if you've gone out of your way to find him you can actually do it.

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