On October 7, 2006, the investigative journalist Anna Politkovskaya was shot dead in the elevator of her apartment block in central Moscow.

A strident critic of president Vladimir Putin, she had worked tirelessly to expose both abuses of human rights in Russia's wars in Chechnya and abuses of power by Russia's ruling politicians and oligarchs. Her story is the subject of Anna, the latest show by Edinburgh Fringe regulars Badac Theatre Company.

The English group define their work as "extreme political art", and anyone who has seen their past productions, such as Ashes To Ashes or The Factory (both about the Holocaust), will attest to the extraordinary power of what they do. However, I ask director, writer and actor Steve Lambert, isn't telling Politkovskaya's story something of a departure for the company? Previous Badac shows have thrust the audience into a moment of violence; this piece would seem to require more narrative.

"Yes, that is the case," Lambert agrees. "It's a bit of a risk for us. It's very different from our approach in the past, when I would take something I'd read about or researched and develop the show from a very physical, visceral idea. When I took on the story of Politkovskaya, I realised we'd have to approach it in a different way, because of the nature of her journey. That said, there are instances in her journey that are violent, moments when she was threatened to an extreme degree."

Lambert alighted on the story of Politkovskaya for reasons very much related to his usual theatre work, he says. "We tend to forget [about the bravery of many investigative journalists], especially in the present climate, in which journalists are not portrayed in the most flattering light.

"I realised that is very unfair - If we're going to do work on human rights abuses, there are journalists who suffer human rights abuses because they try to bring us this news - Politkovskaya highlighted that role more than anyone I'd ever come across."

Not only that, but given Badac's concentration on matters of justice and human rights, it seems appropriate that they should turn their attention to Putin's Russia. From the poisoning of Alexander Litvinenko in 2006 (whose death in London has never been the subject of a UK public inquiry), to the imprisoning of members of the protest band Pussy Riot and the recent conviction of human rights lawyer (and political opponent of Putin) Alexei Navalny on contested corruption charges, Putin is considered by many to be building an increasingly autocratic, reactionary and lawless regime.

"Putin is very clever at what he does," says Lambert, "but he is using nationalism in a way that is almost fascist. That is something that the West should do something about, but they don't because of Russia's oil and gas."

The dramatist's immense respect for Politkovskaya's tenacity, integrity and courage in investigating and criticising Putin and the Russian elite is only enhanced by the fact that she carried out her work in the almost certain knowledge that she was putting herself in extreme physical danger. Lambert has met with both a friend of Politkovskaya, who works for Amnesty International in Chechnya, and the murdered journalist's sister. He asked them both if they thought Politkovskaya knew she was likely to be killed if she continued her investigations. Both said they were sure that she did.

"Despite having that knowledge, she still continued," says the director. "That makes you feel humble. You think, 'If I was in that situation, what would I do?'"

What Lambert does, as a theatre maker, is find a powerful theatrical aesthetic – inspired by the great theatre thinkers Jerzy Grotowski and Antonin Artaud – which puts audience members in close, often uncomfortable, proximity to the violent extremes of human behaviour. He makes no apology for doing so.

"Theatre, to me, should be ugly," he says. "The subject matter is ugly, so, therefore, the actors should be ugly, the drama should be ugly. At the end of it, hopefully, the audience will sometimes walk out feeling ugly. To me, that's important. I don't want everyone walking out feeling lovely about themselves. There is a place for theatre that does that, but it doesn't excite me. One of the things that attracted me to Grotowski and Artaud is that what they're really talking about is ugliness.

"Theatre's about a relationship between an audience and an actor, or a group of actors, and there should be no separation between them. Theatre should be an experience that they share and undertake together. Within that there should be ugliness, grotesqueness and aspects of humanity that we're not used to dealing with - Artaud was barking mad, to be honest, but, nevertheless, he wrote some of the most amazing literature on theatre that you'll ever read."

Badac's Edinburgh performances come at an important point in Politkovskaya's ongoing story. The trial of five men accused of her murder began in Moscow on Wednesday. Her children – daughter Vera and son Ilya – are boycotting the proceedings, which they denounce as illegitimate, both in terms of the rushed timetable and the selection of the jury. Lambert's drama seems more likely to honour the journalist's legacy than anything which takes place in the court in Moscow.

Anna is at Summerhall, Edinburgh, August 2-25, For further information, visit festival.summerhall.co.uk