It was a Bridget Jones moment. British author Jojo Moyes arrived at Los Angeles for a meeting with MGM studio executives in Hollywood, only to pop the cleavage button on her expensive new jacket in airport arrivals.

"I persuaded the security guards to get down on their hands and knees to find it, which they did, once they discovered I was going to Hollywood," the award-winning romantic fiction writer recalls, laughing.

"I discovered that at San Diego Airport, you can buy any kind of tourist tat, you can buy a muffin, you can buy coffee, but what you can't buy is a needle and thread.

"So I basically conducted the first half of the meeting at MGM with my hands crossed across my boobs to try and hide the fact that I had no button.

This was her first experience of the film world, more specifically her first foray into writing the screenplay of her hit novel Me Before You. The movie is due out next June and stars British actors Sam Claflin and Emilia Clarke, who appeared in Game Of Thrones.

"It was the most fun experience. I was taken to the studios in a big black car and shown up to a reception room full of Oscars. I was so uncool. I just asked the receptionist if I could take a picture and she was like, 'OK, you're one of those'. They were all terribly cool, glamorous and smart."

She didn't have time to feel scared, she reflects, although the experience was quite surreal.

"It's mind-blowing. Part of you is having the conversation with studio heads and the other part of you is having a parallel conversation going, 'Oh my God, where am I?'

"When they offered me the chance to write the screenplay, I was a bit surprised, but I've been involved at every stage. I was on set for the three-month shoot, mostly at Pinewood, but also in Spain.

"What I discovered from the process is that I love writing screenplays and I'm still learning."

She's also delivered the screenplay of her novel The One Plus One, which is currently in development.

Hollywood may beckon, yet little more than three years ago, Moyes, now 46, was a moderately successful author with eight novels under her belt. "I'd got to the stage where I was thinking about alternative careers," she admits.

But while driving her children home from school, she heard a news story on the radio about a young rugby player who had persuaded his parents to take him to [assisted dying facility] Dignitas after several years with quadriplegia. From this, Me Before You, her most successful book to date, was born.

It centres on Will, a quadriplegic who wants to die, and his carer Lou, who agrees to accompany him on his final trip.

"The issue of quality of life was very high in my head. At the time, I had two close relatives who both required 24-hour care to stay alive," she recalls. "One had dementia and injuries, the other had multiple sclerosis. To watch someone diminish and know they hated every intrusion, and all the stuff that has to be done to you, is awful."

The book became a massive success and catapulted her career. Some nine million copies of her tales have now been sold worldwide, and she has outsold Jo Nesbo in Norway.

"It became a word of mouth book, and as a writer that's just the holy grail. I would say its sales are 50% word of mouth."

Me Before You's success changed her life. She and her family now live in 22 acres of land in a 17th century house, and have three horses.

"It's nice as a writer to have paid for the roof above your head. I have a son who's deaf, and now he can go to a school that I can pay for. It has very small class sizes, which makes a huge difference to his potential success."

She wasn't planning to write a sequel, but the characters had never really left her head, thanks to the stream of emails, tweets and letters which kept coming from readers telling her their own stories and asking what happened to Lou, and the fact that she had written the screenplay for the forthcoming film.

"I started to ask myself what would have happened to Lou. I didn't think you could go through that and be unscathed."

The book is essentially about grief and what happens if you are left in the slipstream of somebody else's life decisions.

"The characters are all struggling in their own ways with losses that other people have imposed upon them. Lou and her family and Will's family are all having to deal with the aftermath of life without him. I'm interested in what you want and what you are duty-bound to do to the people around you."

The theme of euthanasia has also made her reflect on her own life.

"It's made me do a lot more things that I was probably too anxious to do. I fly all the time now, whereas in the past, I would do anything not to go on a plane.

"I've learned to drive a lorry, I've taken my advanced scuba diving licence. I do things that push me out of of my comfort zone, because the message of the book stuck with me. Sometimes your characters teach your things about yourself.

"I would rather fall out of the sky in a plane than spend 10 years staring at a wall in a care home."

Before taking on the screenplay of Me Before You, Moyes spoke to several screenwriters who are friends and gave her lots of pointers.

"But there is no substitute for being on set, in terms of learning the art of screenplay. You learn that some things that work on the page don't come alive on screen and you have to make some lines work harder. It also depends on what actors are capable of.

"What was lovely for me was being part of that collaborative process."

She sneaked her family - her husband, journalist Charles Arthur, and their three children - on to the set, which they loved.

"I think that was the point at which they decided I did have a real job after all, rather than someone who sits in her pyjamas in the back room tapping away, with her feet on the dog."

She is now on a month-long book tour and is considering a follow-on to the follow-up, After You, but it may not happen for a couple of years.

"Next year, I'm going to do very little travelling, and very little of anything apart from trying to focus on the next book."

:: After You by Jojo Moyes is published by Michael Joseph, priced £20. Available now