'I love men." Of course the first thing anyone notices about Oona Chaplin is the surname.

"I think men rock." And yes, for your information she is related. She's Charlie's granddaughter. "Most of my friends are men." But in person she is so much more than that. "I was always a bit of a tomboy." She's sparky and saucy, full of sass and fire, as happy to talk Marxist politics as gender politics. "It's just a simpler existence." And now and again she just opens her mouth and something wild will tumble out. "Having a penis makes thing easier."

Ahem, as I was saying. Anyway, we'll get to the surname later. But on the first decent day of spring in London Oona Chaplin, 27, has cycled into Soho in a crop top, high-waisted trousers and a kind of all-round juicy, joyous insouciance to talk about her international life and work, going to Gordonstoun and the contradiction of growing up rich and growing up with leftist politics. On screen you may recognise her from her role as Dominic West's impeccably soignee wife-turned-TV-chef in the BBC Two drama The Hours or as Talisa Maegyr in Sky Atlantic's Game Of Thrones (which I can tell you nothing about as I've never watched it). In person she's a real-life screwball comedy heroine, all full-force quirk and chattiness.

You've come in as she's discussing men, as you may have gathered. (I'm going to stop interrupting now.) "There's less - I dunno - calculation," she continues. "It's much more of a straightforward existence. However, when I do meet a fantastic woman I never let her go. I have a wonderful harem of women who I call my 'wives'. I have six wives currently. When you meet a woman that makes you champion the female species it's so wonderful and so inspiring and great.

"But as a general rule I think men are pretty rocking. Also, I quite fancy most of them."

In this Chaplin is slightly different to her most recent character, in Bryan Elsley's new Channel 4 drama Dates, where internet dating is the theme. She plays Mia, all lithe limbs, clinging dresses and corrosive acidity. "She's different to me in that she's not so keen on making people feel good about themselves. She doesn't give a f*** most of the time. So that was quite challenging and quite fun to do that, just throw criticisms at men and not bat an eyelid. It was very hard. I kept wanting to apologise. I was fighting every instinct in myself."

I'm presuming Chaplin's own dating history is a tad different. "I've never had a date." Come again? "I've never been on a date at all. Not in the conventional sense. I've hung out with guys on a one-to-one basis, but I've never been on an official date. Generally speaking, I decide whether or not I'm going to be with somebody before I spend any time alone with them. They get vetted by my friends who go: 'Oh God, he's not the one.'"

It's because she's not British, she reckons. "I suppose I've got quite a different cultural heritage and I look at relationships very differently to the people in this country."

In what sense? "It's very simple. It works until it doesn't. Here, there's all these rules about semantics; about when somebody becomes your girlfriend, the rules of when you kiss and when it's acceptable to sleep with someone. And until you have the exclusivity chat you see a number of people, which I would find impossible - because - I don't have the organisational skills, mainly.

"It's more uptight here, I find, whereas in Cuba it's like: 'I like you, let's go and have a kiss in the bushes.'"

Ah yes, Cuba. She was conceived in Havana, "as my parents incessantly remind me", born in Spain and spent her childhood shuttling between Cuba, Spain and Switzerland, where her grandfather had exiled himself and where her grandmother, also called Oona, Charlie's fourth and final wife (as well as American playwright Eugene O'Neill's daughter) lived. Their daughter – Oona Jr's mother – is Geraldine Chaplin, herself an actor of some renown who has worked with everyone from David Lean to Pedro Almodovar (and even appeared in Chaplin's film Limelight). Chaplin, then, comes with a history.

When was she first aware of the weight of that surname? "Very early on. I remember a girl crying because she was so happy that I was a classmate, which kind of gave me a Jesus complex for a while. Not really, actually. I was just confused."

She did consider changing her name for a while when she became an actor. For a while she considered a surname drawing on her other grandmother's Mapuche Indian background. "I was looking at Oona Nany. Oh God, Oona. How unbelievably pretentious." But she had a conversation with her mum and her principal at RADA, who told her a "pretty girl wouldn't cut her face into pieces so she can say 'they're not hiring me for my looks'."

And anyway, she's proud of her heritage. "I took on the responsibility of honouring it and not having my granddaddy turning in his grave. That's the objective now."

Chaplin's father is the Chilean cinematographer Patricio Castilla, the first person to ask for political exile in Cuba. Politics was clearly part of the story then. "Oh yes, completely. I read Das Kapital when I was nine, obviously not understanding a word of it. But yeah, it was a very political family, lots of interesting people to dinner. We would constantly have great minds in the house talking about big ideas, and it was a really wonderful way to experience grown-uppedness as a child."

Although she has now lived in London longer than anywhere she remains at heart a Latina, I think. Her English is perfect, but now and again she breaks off to think aloud in Spanish. She goes back to Cuba all the time. "I communicate a lot better with the people there, I think. It's a much more visceral understanding. I don't need words. I feel I probably identify more culturally with myself there than in any other place, although in Cuba I'm still a foreigner.

"It's a different way of life and it's much simpler. That's such a cliche and I hate it when people say that, but it is. It's much simpler because your problems are real. Your problems are: 'The electricity's gone again. What am I going to do with the food in the fridge?' Rather than: 'Oh, my career. Where do I want to get to?' 'What is the perfect man?' There, you're just happy to get a shag. You've got different priorities."

Presumably it's changing under the current liberalisation policies being pursued by the Cuban government led by Raoul Castro, Fidel's brother, I suggest. "Yes, but I think the change is mainly coming from YouTube and travelling. Unfortunately, the changes that are happening right now leaning towards capitalism aren't actually based on anything except consumerism, which is really sad. The generation below me is incredibly materialistic. I don't think most people know what it takes to survive in a world like this, just as people here don't know what it takes to survive in a world like that.

"I would love to give Cuba capitalism for one year. 'Right, go. See what it's like. Oh, you have to pay for your house now? Yeah, and school and uni.' It would be quite an interesting experiment, actually. I might write a letter to Raoul."

Clearly she's her father's daughter still. Actually, she dotes on her parents. The affection for them shines out of her. Yet it sounds like she put them through hell in adolescence. What kind of teenager were you, Oona? "A horrid one. I don't think I became a nice person until I was 19. That's a lie. I did some nice things. I think I was just very confused. I think it's very difficult to grow up with the ingrained juxtaposition of a left-wing family and a privileged upbringing. And I think that created a lot of conflict in me at every age, because I understood from very young that having a social conscience and yet going home to your beautiful house is a difficult thing to live with. It's only recently that I've kind of accepted that you do what you can and you're grateful for what you have.

"But, yeah, I was very rebellious because I had a lot of anger. Hormonal anger. I'd get premenstrual three weeks in advance. I didn't have a reason to be angry. My parents were adorable, my life was great, I was good in school. Everything was fine so I had to create my own problems. I had to justify the angst.

"I got dreadlocks and I started eating so much and I got really quite overweight and I just hated my parents. But I have apologised profusely to my parents. I know that I made my dad cry once and that was f***ing hard to deal with because he's a man. He's a man! And that's the moment when I realised I needed to leave the house. 'I know I love you, but I hate you as well and I need to go and focus my hate on something else because I'm making you suffer and you've been nothing but wonderful parents.' So - I was a handful."

And so she went to Gordonstoun. "I made a very conscious decision to be the most quiet and mysterious person there." How long did that last? "About three weeks."

When she did start speaking she started lying. "I made up another brother who was gay because I wanted some gay in my family. As soon as I arrived I realised everyone was posh. I made a really broad judgement over everyone, completely ignoring the fact I was also from a privileged background. And I took it upon myself to be a lone ranger on a mission to educate these protective, naive little children about the real world. But I think everyone knew I was lying as well. I hope they did. I hope they weren't foolish enough to believe me."

Despite all that teenage drama she rather enjoyed herself in Scotland. What she remembers is the landscape, the woodlands, "where you could get up to mischief", and the cliffs. And dancing Scottish jigs and drinking Irn-Bru. And vodka. And whisky. "Whisky was my drink. I used to go into the White Horse in Elgin and ask for scotch on the rocks and think I was really hardcore. I don't think I liked it at the time, but I grew to like it."

And then there were boys. "I arrived not having even snogged anyone before and within a couple of weeks I knew that wasn't going to float. So I was anyone's up there. You just said a kind word to me and I'd have kissed your face. There were really good-looking boys as well. And we had a wonderful thing called the Gordonstoun goggles. People who, if you see them outside of Gordonstoun, you'd never fancy but in there it's, 'Oh my God, you're fit.'"

When did she begin to resolve this contradiction she felt between privilege and politics? "Umm, it was probably around the same thing as my acting. Because at the beginning I felt this undeservedness that came along with the name. Even though I went to RADA and worked really hard and wanted to take what I did seriously, even then I felt I didn't deserve it because someone else is more talented and better.

"So I sabotaged quite a lot of auditions in the beginning. But then – this is so cheesy – my cousin has practised Buddhism for a long time and it was through conversations with him and beginning to chant I realised that it's not about apologising for what I've been blessed with but making the most of it and doing what I believe in, which can be acting or anything else. Your profession is only a fraction of your life." That said, there's no suggestion she would want to do anything else. Ask her why she likes acting and there's no earnest, considered response. "It's just so much f***ing fun," she roars. "I play pretend for a living."

So what have we learned? That Oona Chaplin speaks four languages (English, Spanish, French and Italian), loves her parents and admires her grandfather. Oh yes, and that her surname may be the least interesting thing about her. n

Dates begins on Channel 4 at 10pm on Monday and continues on Tuesday and Wednesday.