Though the way we respond to the overt racism in Shakespeare's tragedy Othello has changed since it first premiered 400-odd years ago, there is no doubt that the themes of fear of the outsider and racial prejudice are still directly relevant today. But what is so interesting about Ellen McDougall's scorching and superb new production of the play - aided with dramaturgy from Joel Horwood - is how, though there's still a focus on race, McDougall also brings out the piece's inherent, gruelling misogyny.

The women are much more present in this version of Othello, which has a lot to do with the gender swap of Cassio, the soldier with whom Othello's innocent wife Desdemona is accused of having an affair. The piece starts with Michelle Cassio, silently getting dressed into her armour, pulling on her boots and tying her hair back from her face. She is the vision of a woman alone among men in the business of war.

Desdemona too is central to this play. Though she does not appear for the first few scenes, her name hangs about the action until she is brought in by Othello, in order to prove to the Duke that she has freely married him. Natalie Klamar plays her as no pushover. While loving to Othello, she is also fierce and confrontational, and she bursts with anger in the bedroom scene at the end when she realises how foolish Othello has been. She is no less angry when she finally realises that her words are the only things she has between her and a vicious end.

Desdemona's trusting relationship with Emilia is also very convincing and in the final scenes Thalissa Teixeira gives a brilliant scream of desperation as she finds her voice - hitherto silenced by the awful bind she has to her abusive husband – where she denounces Iago as a monster and Othello as a murderer.

Both Kurt Egyiawan's Othello and Sam Spruell's Iago are men undone by their own insecurities. They are horribly blinded by what they think is the right way to behave in a masculine-driven society. And in a way, though you never excuse either Iago or Othello, there is a sense that they are victims too.

In the second half McDougall bleeds scenes into each other, playing them out while other characters - Desdemona and Emilia, for example - stay still in the background. It works well, showing each moment of deception within an overall whole. You are never allowed to forget the ultimate outcome of Iago's plottings – the pointless death of two women.

In a production littered with ruffs and rapiers, where the men wear bulging codpieces as if they were trophies, there are more than a few surprising modern references. An choir sing beautiful a cappella arrangements of modern pop tracks such as Katy Perry's "I Kissed a Girl" and Britney's "I am a Slave 4U". An intense and very changed version of Lana Del Rey's song about obsessive love "Video Games" haunts the action, popping up in moments of quiet tension between Othello and his wife as well as the darkly abusive moments too. Later still, in the wake of the play's violent, bloody climax McDougall has us listen to the choir's version of PJ Harvey's "In the Dark Places" in blackout. It is a chilling moment which reminds us that this play is not just one man's tragedy but society's as a whole.

Othello runs at the Sam Wanamaker Playhouse at Shakespeare's Globe runs until 22 April.