The typescript of Bryony Lavery's latest play ends with a triumphant phrase in bold print: "Draft – Thursday!!!! – May 31st 2012". As the play is called Thursday, I guessed that the four exclamation marks reflected the neatness of having completed a play with that title on that particular weekday.

"Oh!" she says, sitting at the kitchen table in her home in East London. "How strange. I hadn't made that connection. No. It was finally deciding what to call it. We had an awful time getting a title and I foolishly opened it up to discussion. Then I realised that, in the end, it's about an ordinary day and Thursday is about the most ordinary day of the week there is."

Except that, in this play, the day is anything but ordinary: it's Thursday 7 July 2005, when three London tube trains and a bus were blown up, resulting in the deaths of 52 passengers plus four presumed suicide-bombers, and 700 injuries. What was first thought to be a local news story – a power-cut was initially blamed for the chaos – rapidly became international. It might at first seem surprising that Thursday is being premiered in Adelaide, Australia, but it is loosely inspired by the story of Gill Hicks, an Australian who lost both legs in the attack on a train travelling between King's Cross and Russell Square.

Thursday is a co-production between English Touring Theatre and the Adelaide-based company Brink, run by Chris Drummond. He auditioned a number of potential playwrights, giving them a copy of Hicks's book One Unknown as source material. "My eyes filled up when I talked about the event," says Lavery. "And I came away thinking: 'I'll be really upset if I don't get this. This is mine.' And luckily they decided it was."

A downloaded boarding pass is neatly tucked inside a passport on the kitchen table: Thursday premieres at the Adelaide festival, Australia, from 28 February (the Guardian is a media partner of the Adelaide festival, supported by Emirates) and Lavery is flying to Adelaide to begin rehearsals. The play was created during workshops in London, some of which Hicks attended, but the script is fictional, with the central character of an Australian expat given the name Rose.

That decision is significant because Lavery, who has often worked in fact-based drama, became involved in a distressing dispute over the provenance of Frozen, her most commercially successful play, which was performed at the National theatre in London in 2002 and nominated for a Tony award on Broadway in 2004. A fictional account of a young girl tortured and murdered by a serial killer, it was accused of potential plagiarism, because it used material from a Malcolm Gladwell article in the New Yorker and a biography of an actual psychiatrist. After talking to Lavery, Gladwell later exonerated her – but I wonder if the experience had made her wary of dramatising fact?

"I'm a lot more careful, obviously. Most of what happened with Gladwell was really a boring story of things not being checked for rights and so on. So, on this occasion, with Gill Hicks, I did say: 'Has all this been cleared?' I never want to upset anyone in that way ever again. But it did also become very clear to me, working on Thursday, that, although you may seem to be creating people, you are making constructions which can seem to be real. The challenge was to create a character who acknowledged the spirit of Gill, but wasn't Gill."

Discussion of "appropriation"The subject reminds Lavery of a lighter incident of alleged life-theft: "I did a play called Family Album when my mother was alive and I thought I'd made it all up and, in the script, the mother has a dog put down. My mother read it and she said: 'But you know why I had to have that dog killed.' And I suddenly realised that I had somehow picked up that story or memory." She laughs. "It was the start of an ongoing lesson about the use of other people's stories in drama, which, goodness, I've had to learn!" Her mother subsequently saw the play and "understood that it was fiction, but also became rather proud of having been the source". There is often an additional complication of ownership in a Lavery play because, ever since her early work with companies such as Female Trouble and Gay Sweatshop, she has often worked collaboratively – a process that continued with Thursday. Does she have the final edit? "Pretty much so. It's usually a negotiation with the director and, in America, it's often a negotiation with producers as well. On Broadway, a producer will often say, 'that scene needs to be cut.' But, really, it's very rare for everyone working on a scene to disagree."

A key decision during the process of working on Thursday was that the perpetrators of the murders are not dramatised: "I had quite a lot in early drafts with a character who was one of the terrorists, but dropped it. We opted to go for the sheer diversity of people who would have been on that train in a multicultural city such as London. So we have a young Asian woman whose biggest fear is telling her mother that she's a lesbian."

One of the most impressive aspects of the play for me is that Lavery has avoided the problem common in American dramatisations of transport tragedies – such as the 9/11 plane attacks – that all the passengers are retrospectively made into saints. In Lavery's play, some of the doomed have irritating personalities, gross lavatorial habits and appalling sexual thoughts. She nods. "Yes, absolutely. That's why I wanted the freedom of fiction. If you are writing 'The Gill Hicks Story', there are inevitable restraints. But I'm across in a sort of parallel corridor from the real events."

In common with a number of modern dramatists, including Caryl Churchill and Martin Crimp, Lavery uses vertical slashes and bracketed overlaps in an attempt to bring theatrical speech closer to the messy interruptions and near-incoherence of actual conversation: "I'm quite dictatorial about how the words are set down on the page, trying to capture the strangeness of spoken language. But it is finally a device. In real speech, people tend not to interrupt at exactly the right moment dramatically, so that the crucial words are heard clearly."

Thursday introduces a new dialogue concept, in which, for example, a line will be prefaced: "SOMEONE>ROSE (actor playing Chrissie"), which means that the bracketed performer speaks Rose's inner thoughts; at different times, the main characters are all given such doppelgänger inner monologues. In the first draft, Lavery tells me, there were two different characters called Gill Hicks, waking up in London and Adelaide, and two men called Jermaine, one a terrorist and one not, starting their days in Surrey and Pakistan. Eventually, during workshops, the doubles disappeared, and the commentary was handed over to other characters.

"I like there to be a surprise in the structure or, otherwise, where's the fun?" she says. "Although one of the actors has already complained, jokingly: 'All of my character's best lines are said by someone else.' So it will be interesting to see how that works. My American agent didn't get it at first."

I finished reading the script on the tube to Lavery's part of London and, despite suffering a mild panic attack at the conjunction of subject-matter and transport mode, was struck by how quickly the tube has become routine again for most people.

"Yes," agrees the playwright. "We forgot very quickly. During the workshops, the Australians who were taking part were staying near Russell Square and they did a double-take, recognising it as one of the locations, but we realised we hadn't even thought about it. It's interesting that we don't keep the event going in the national consciousness in the way that Americans did with 9/11."

Although Lavery has lived in London for most of her adult life, she still, at 65, has the distinct tones of her Yorkshire birthplace. Does geography feel important to her writing? "Yes. I think I do think of myself as a Yorkshire writer, although I also like to explore other ways of speaking as well. I left when I was 18, and it's more significant to me now that I live in a big city. But I think the northern phrasing and spirit are through me like seaside rock."

Over the years, Britain's male playwrights have often formed dining clubs or cricket teams. Is Lavery part of any dramatists' gangs? "I don't know many writers of my generation because I started very late," she says. "I used to stay at David Edgar's house when we worked at Birmingham University together. He used to serve tea in the morning in quite a short dressing gown. He has the best legs I've ever seen on a man!"