How We Met: Lucinda Coxon & Olivia Williams

'Going to see plays with her is scary, as she's so bright. I wait to hear what she says then agree'

Lucinda Coxon, 45, is a playwright and screenwriter. Her plays include The Shoemaker's Wife, The Ice Palace, Wishbones and Waiting at the Water's Edge. Her screenplays include The Heart of Me and Happy Now?. She has a daughter and lives in north-west London

The most striking thing about Olivia is that she's not the person people imagine her to be. Because she is quite posh and clever, and rather beautiful, people find her quite intimidating, and imagine she's a bit chilly, because she has a slightly glacial, goddess thing going on. That is actually very unlike who she is: she's a very warm, funny, spontaneous and surprisingly down-to-earth person.

I can forget she's a star, so when I'm walking down the street with her, and people approach us, I always think they've come to ask directions. I'm amazed when they want her autograph. I also forget that she's very beautiful, as she's remarkably normal, but every now and then in rehearsal, the light will catch her at a certain angle and you think, "Dear God! That's a massive genetic advantage you've got," because she's suddenly completely luminous.

We met in 2002, when she was cast in a film I wrote called The Heart of Me. I wasn't at Olivia's audition, but I spoke to the director and producer on the phone after they met her; the director said she was terrifying and that she told him how to make the film. So I was slightly braced when I met her. But as soon as we did meet I realised we had a frightening amount in common: we both have an exasperating mixture of toughness and fragility and we're both quite hard on ourselves.

She is incredibly committed to her work, and once she gets behind a project, her loyalty is remarkable. She's like that as a friend as well. There is a real sense that a friendship is a decision and when she's decided you're a friend, it doesn't all go out the window if the wind blows.

We talk about projects she's not involved with, too, and she'll say, 'Oh you know who would be great for that, I can get it to him'. She'll really help other actors get jobs, which is frankly unheard of.

Olivia is also a person I've wounded up confiding in – she asks you how you are and you say you're fine, she gives you the look and you just blurt out the truth.

She's always there; she's not a fusspot, but is incredibly dependable. And this in an industry where that's not fashionable.

Olivia Williams, 39, is an actress whose film credits include Rushmore and The Sixth Sense and is soon to appear on stage in Happy Now?. She lives in London with her husband and two children

The first thing I knew about Lucinda was her writing, because I read the script for The Heart of Me. I loved the precision of it. She really reminded me, in the way she chooses words, of the writing I love most – I'm a huge Jane Austen fan and she has the same economic way of taking the piss.

I think I was probably expecting an older, spikier person, because the play is incredibly insightful about long-term, grinding disappointment. But instead she has this mane of dark brown hair and this sexy presence, and I liked her immediately.

We struck up a conversation on the set and we just got on. It was so instant – although there was a divide between us in that she was a mother and professional woman and was balancing a career. In the intervening years I've crossed the divide from being a single woman, having a career and going in search of love, to finding love, finding a husband, having two kids and then trying to run a career as well. We have become much more similar and our friendship has re-exploded.

There's something that happens to your female friendships when you have children. There's an idea that you'll meet up and your children will play, but you meet and you don't get to speak to each other. But our friendship is almost like a guilty pleasure because I don't know her partner and I don't know her daughter and she doesn't know mine that well. It really is a grown-up female friendship.

If Lucinda had chosen politics or astro-physics as her speciality we'd all have to watch out. She would be running the UN, or designing the next space exploratory equipment, and she would make sure that it got funded. Another thing I love about her is that while I'm not very in touch with feminism, it is in her fibre to explore female achievement and to write about female experience. And not in a way that is exhausting or alienating for men – she is celebratory about the female experience, and very funny and incisive about it.

Going to see plays with her is scary, because she's so bright. I wait to hear what she says before going, 'Yes, I completely agree.' I'm in awe of her. She's so bright and sharp that a lot of people are afraid of her, but she's incredibly loyal and sensitive and she stands up for her mates.

In a way I'm still slightly ashamed to be, I'm a bit of a groupie of hers because she is like the head of the ultimate girl gang. It's probably as well we didn't meet at school because I would have been horribly sycophantic. She is the person you follow, who's brave enough to stand up and say what she thinks, and she says it so well that it really does quell any objectors.

'Happy Now?': National Theatre, London SE1 (020 7452 3000, www.nationaltheatre.org.uk), from 30 January to 15 March