Sandy's Boxing Gym in Craigmillar might not know what hits it this week when Common Wealth Theatre Company move their new show in there for its Edinburgh Festival Fringe run.

No Guts, No Heart, No Glory, after all, isn't a typical look at the power and the glory of one to one combat inside the squared circle. Evie Manning's production of Aisha Zia's script is not only about women boxers, but Muslim women boxers who also happen to be champions.

"It all stems from Our Glass House," Manning says of Common Wealth's previous Edinburgh show, a site-specific piece about domestic abuse performed in an empty house in Wester Hailes. "After we did it, we had a lot of conversations about representations of women onstage, and we decided that we wanted to focus our next piece on strong role models for women and what they can achieve."

With Zia also keen to do a piece based around young Asian women, Manning somewhat fortuitously met a Muslim neighbour in Bradford who was a boxer.

"That really challenged my expectations about why I should be surprised that she's a boxer," says Manning. "Then I discovered there were two national womens boxing champions from Bradford who were Muslim, and they both ended up getting involved in the project, which fitted perfectly.

"Presentations of Muslims on TV or in the theatre are usually about extremism, or about women staying at home. We worked with young Muslim men and women, and asked them how they thought people saw them, and the answer that came up most was that that they thought most people thought they were terrorists. How do you change that perception? We wanted to do something to show Muslim women in a different light, and show that they could be inspirational and become role models."

In this respect, No Guts, No Heart, No Glory is a kind of flipside to Our Glass House. Based on real life experiences, Zia's text and Manning's production transformed these into a series of up close and personal vignettes performed simultaneously across each room in the house, with some spilling up or down the stairs and criss-crossing each other. However impressionistic its rendering, witnessing the play in such close proximity made for a devastating experience, and when its final scenes tumbled out onto the streets, it was almost a relief to follow it outside.

"We want the audience to be active," says Manning, "so we have to try and say something to how the audience is feeling, and respond to the building we're working in as well."

The Common Wealth aesthetic has been developed since the company formed as a loose-knit collective of artists in 2008.

"We were very DIY," says Manning, "like little punks just taking over abandoned buildings and transforming them, putting on big-scale shows, political, ambitious epics that were a bit wilder than we are now."

These early works included taking over Bristol's old courtroom for The Ups and Downs of the Town of Brown, a large-scale reimagining of Bertolt Brecht's The Rise and Fall of the City of Mahoganay. Common Wealth also moved into a disused zip factory in London's east end for An Indecent Incident, a riotous, vodka-fuelled take on Dostoyevsky's A Nasty Story. Since then, the company's reckless spirit may still be intact, but they have honed things somewhat.

"By the time we got to do Our Glass House we were a bit more mature," is how Manning puts it, "and found that we wanted to do something about social change, and wondered how we could apply all this stuff we'd learnt to doing that."

By Manning's own admission, Our Glass House, which toured to other cities in the UK, was "a game-changer. It was site-specific, but more importantly we learnt how to work with people who lived on the street we were working on. Taking things out to Craigmillar or Wester Hailes rather than regular venues is a very deliberate choice, and is part of us trying to do theatre differently.

"We had this amazing relationship with the people in Wester Hailes, where they can feel left out of the Fringe, but where it's important that they're part of it too. The boxing community as well have been amazing. Any gym we approached have been totally up for it, and want to promote womens' boxing."

In some ways, Common Wealth are a refreshingly vital throwback to what fringe theatre used to be like, with a messy, anti-establishment and unashamedly socialist ethos at the company's core. This should be made even more explicit in the company's next work.

Commissioned by National Theatre Wales, Nationalisation! is a community-based project which asks participants in Merthyr, South Wales, to imagine they have reclaimed control of all public services from private hands to run them collectively. As with Our Glass House and No Guts, No Heart, No Glory, this promises to go beyond polemic to make its point.

"It's an experience and an event," according to Manning. "It's the emotional journey that's the important thing. There'll be lasers and a powerful sound score in No Guts, No Heart, No Glory, so it really feels like a gig.

"There's a narrative thread that runs through it, but I'm more interested in audiences going away with a brand new energy."

No Guts, No Heart, No Glory, Sandy's Boxing Gym, Castleview Community Centre, Craigmillar, today to August 25, various times.