‘I always try to say this without sounding like a nutter,” says Cathy Brown, “But I remember when I first knocked someone out, it felt amazing. I can’t lie. I was like: Oh my God, you’re so powerful!” Cathy “The Bitch” Brown is a pioneer of women’s boxing and one-time world No 3, and she’s telling me what it feels like to be very, very good at punching. “It’s the connection,” she says. “Whether it’s a pad or someone’s face – that sounds really bad – it’s like a release of everything evil [in you]. You know the Exorcist movie, “Demon, begone!” It’s like that, releasing all these demonic internal feelings.”

Even in our times of supposed gender equality, there’s still often a flinch of discomfort when we hear about women beating each other up for sport. The boxing world itself was long resistant to women’s participation. Brown got her professional licence in 1998, only the second woman to do so, and female boxers were only admitted into the Olympics in 2012 (when, of course, Britain’s Nicola Adams took the flyweight gold).

The unease, and sometimes outright opposition, that surrounds female boxing is at the heart of two plays soon to be seen in London: Libby Liburd’s funny, forthright Fighter, and Joy Wilkinson’s investigation into the world of Victorian women’s boxing, The Sweet Science of Bruising.

Fighter is partly inspired by Cathy Brown’s battle to be accepted as a woman in the ring, and it’s the story of a single mother, Lee, who’s fighting more than just her opponent. A celebration of courage, heart, pain and hard work, like Liburd’s previous piece Muvvahood, it’s also a show that comes out of her own experiences. Liburd took up boxing herself just over a decade ago, when she was looking to do something more challenging than Body Pump sessions at the gym. She found a women’s boxing class in east London and as her training progressed, graduated to fight on the white collar circuit.

“I remember the first time they put me in the ring to spar with a girl who was really experienced,” she says. “The trainer basically said: I just need to see if you can take a punch without crying, if you’re going to stay upright. So that was what I concentrated on, staying upright, and I stood there while she battered me, basically.”

She vividly remembers the first punch, and it wasn’t her that threw it. “That first punch on the nose is like, ‘Ooooarghhh’, your eyes water,” she says, likening it to getting her nose pierced. “There’s a moment of ‘What do I do with this?’ and then you’re there, you’re present. It’s more shock than pain – you’re already in a lot of pain anyway, from the intense training, and my pain threshold is very high. I know that because I had a three-day labour,” she says. “It wasn’t even accepting the pain, it was relishing it. Because pain is that connection to your body, being in the moment.”

Liburd talks about boxing the way other people talk about meditation. “In this day and age you can be in your head a lot, always looking at your phone. When someone’s punching you and you’re trying to get out the way, you are 100% in the moment, 100% connected to your body. You’re not going: Oh, I wonder if so-and-so got my email?”

Liburd competed in three fights, winning the third, until injury and acting work got in the way, yet she found a home at the gym. “I felt like I belonged,” she says. As a single mother, crucially, Liburd could take her son with her. “Even though there was sexism, I was accepted as a mum in there. My son was about eight at the time, and it was important to me that he could see me doing something hardcore.”

Some people had a problem with her presence. They don’t like seeing women bleed, says Liburd. “Traditionally, men have wanted to protect women, so to send a woman into a situation where she is potentially going to get hurt causes quite strong reactions, to this day.” But the pugilistic urge among women is nothing new. As far as we know, women’s boxing dates back to the 1720s, as playwright Joy Wilkinson discovered when she began investigating the subject, leading to a play, The Sweet Science of Bruising, which debuted last year and is about to be staged at Wilton’s Music Hall.

“I have always been fascinated by the contradictions in femininity and violence and power and women’s bodies,” says Wilkinson (whose writing credits include Jodie Whittaker’s Doctor Who). “Right from the first time I saw Ellen Ripley in Alien or Sarah Connor in Terminator, to see these powerful women taking control of their bodies.”

She was drawn to the Victorian period in particular, when women were at their most corseted, in more ways than one, and “dressed like the furnishings of their domestic abodes”. In the 1860s, when the play is set, women were virtually written out of the history books – the men who ran the sport became better known than the women who took part. That meant Wilkinson was freer to create her own characters, albeit rooted in her thorough research, where she found stories of bare-knuckle, backstreet fights, “the women like Amazons with their tops ripped off, clawing at each other”.

Wilkinson’s characters all come to boxing for different reasons. One is a tomboy following her brother into the sport; another breaks out of her cosseted, comfortable life in search of autonomy; one is a canny prostitute who does it for the money; another a blue-stocking suffragist who sees boxing as the embodiment of breaking down gender barriers. “One’s coming at it from the head, one from the heart, one the body and one a more spiritual side,” says Wilkinson.

The aim is to bring some of the charged energy of the ring to the stage. “In theatre, I’m always striving for that live-ness, that drama you get at a sporting event,” says Wilkinson. “Being in the moment and not knowing what will happen, boxing is one of the most extreme versions of that.” The cast are all actors, but they’ve been training hard with fight director Kate Waters. In Liburd’s Fighter, alongside actors David Schaal and Cathy Tyson, are young boxers who’ll be doing training drills on stage, to bring the authentic sweat of the boxing gym into the theatre.

Those boxers come from Fight for Peace academy in Newham, an organisation that offers personal development as well as boxing classes to young people. They’re not the only ones boxing for a better world. Cathy Brown is currently working in Iraqi refugee camps teaching boxing to Yazidi women who have fled horrific abuse at the hands of Isis. For Brown, who took up boxing after suffering an abusive relationship, the sport was a route to empowerment, and she’s hoping to help others in the same way.

For all its combative nature, ideas of community and belonging come up again and again when talking about boxing, even if in the end only one competitor will triumph. “One of my friends saw the play,” says Wilkinson, “and she said to me: ‘God, I want them all to win!’”

• Fighter is at Stratford Circus, London, 25-27 April. The Sweet Science of Bruising is at Wilton’s Music Hall, London, 5-29 June