Ms Newton said she felt compelled to speak out about her experience after talking to Ms Cox, because she was not the only person affected.
"Your tagline can't be empowering all women when actually all you're doing is taking from them," she said, adding that she was not seeking compensation but rather for Sweaty Betty to be accountable.
"It just feels like for me all the slogans I'm seeing are coming from other female founders.
"I just want them to do the right thing and just morally acknowledging what they've done isn't great and to do better really."
Sweaty Betty said it chose words "to empower women through fitness" to advertise its femtech range, something many brands try to do, which "sometimes… means the language used by different brands aligns".
"We have been using the phrase for over a year and Nixi has not been in touch with us about our use of it. The phrase is used by many brands in various forms and that is why no individual or brand can claim exclusive rights to it or trademark it," the company said in a statement.
"It is never our intent to take credit for the work or creativity of others, particularly from trailblazing women, and we have reached out to Nixi Body directly to convey this. We have also been undertaking a review of all our campaigns and marketing language to fully understand the origins of the phrases we use and will continue to do this.
"We note that such a review was conducted with respect to the 'Wear the Damn Shorts' phrase and its origins date back to at least as early as 2019, before either Ms Cox or Sweaty Betty first used the phrase. We continue to work towards a resolution with Ms Cox, as has always been our objective, however this dispute remains ongoing."
