Mike Bartlett – the talented theatre director and writer, whose new adaptation of Euripides's classic tragedy Medea opens at the Citizens Theatre on Thursday night – is late.

Forty minutes late, to be precise. His schedule has been hit by the tardiness of an earlier interviewer.

It doesn't matter, I assure him when he arrives at the Gorbals playhouse. When we're done discussing Medea and her brutally imaginative revenge, I'll simply arrange for a poisoned garment to be sent to the offending journalist's home.

Apologies and pledges of violent retribution out of the way, I ask the director and adapter how he has approached the thorny question of how one stages an ancient tragedy for a modern audience.

His new script, he tells me, is set on a contemporary, new-build, edge-of-town housing estate. It recasts the blue-blooded Medea and Jason as a 21st-century British couple whose hopes and dreams are invested in the ideas of home and family. Medea's world comes crashing down when Jason leaves her for another woman.

While traditionalists will, no doubt, howl at Bartlett's temerity, I'm struck by how similar the concept seems to some of the plays of the late, great American dramatist Arthur Miller. Like Miller, Bartlett is holding to most of the rules of tragedy (as outlined by Aristotle) but, like Miller, he is also saying that the anguished essence of tragedy holds as true for so-called "ordinary" people as it does for the high-born.

"I hadn't thought of it like that," the director says, "but you're right. So many of those plays, like A View From The Bridge and All My Sons, take place within a domestic context which is not dissimilar from what we're doing."

What Bartlett is doing, he explains, is attempting to build a bridge between Euripides's tragedy and contemporary British society. "I'm not necessarily trying to say anything about class. It's just about wanting the play to connect with an audience, and removing the barriers that might prevent that."

The director is not, he insists, trying to make his characters, in that oft-repeated phrase, "speak in the language of the street". This is not Medea by way of EastEnders. Rather, and more subtly, he is aiming to capture the poetry in modern-day speech.

"I hope that I've written the characters speaking as people speak now. My script includes 'anyways', 'becauses', 'actuallys' and 'ers'. I find if you write contemporary language truthfully and you get it right, sometimes you end up with something on-stage that is a bit poetic. You can hear rhythms in the dialogue which are fascinating."

In order to make an adaptation such as this work, you need exceptional actors. Bartlett and the production's co-producers (the Citz, London-based theatre company Headlong and the Watford Palace Theatre) have certainly attracted some big names.

The cast is led by Rachael Stirling (whose many TV and film credits include The Bletchley Circle, Tipping The Velvet and Snow White And The Huntsman) and Adam Levy (who has been in everything from Coronation Street to Holby City to Rome).

"I wanted to find actors who I can collaborate with and who bring something interesting to the table," the director comments. "The role of Medea is like Hamlet in that it gets much more interesting if the actor has something to bring to it. That's particularly true of a new version of the play."

Bartlett (whose stage adaptation of Chariots Of Fire is currently running in the West End) has been greatly impressed by Stirling's commitment to the role and her enthusiastic engagement with one of the greatest and most difficult female characters in world theatre.

"Rachael's brought a huge amount to it, in terms of her ideas, her personality and her energy. That has changed the text, and it will continue to change the production. She loves this role, I think. She hasn't done anything quite like it before.

"That's what you want. You want everyone to be working hard on a show, and for it to mean something to them.

"For Rachael, as for any actor, this is a tough one. It's hard work to get to the emotional and psychological place that Medea gets to in order to be able to do what she does at the end of the play.

"She has to do that while delivering huge speeches; often, in my version, at speed. And she's in nearly every scene. It is one of those roles which, as an actor, you half run towards, and half run away from."

If Stirling has run boldly towards her character, that is perhaps down to Bartlett's distinctly modern approach to the gender politics embedded within the play. "It feels exciting to charge the play with a big dose of now," says the director.

"We're not in a world where we can just say: 'Women can have it all, a career and a family.' We have enough evidence that that is either too difficult or is based upon having enough money to be able to do it.

"A lot of women find themselves having to make very difficult choices. In this version, when Medea talks to Jason after he's left her, she tells him that she made a set of choices in order to make their lives together work, and he then destroyed everything.

"What we're finding is that by doing it that way, we don't move radically away from the play, but we actually serve the play."

Medea runs at the Citizens Theatre, Glasgow from September 27 to October 13, www.citz.co.uk