Chief executive Mark Davyd wrote on Facebook that Simco, a company mainly owned by Cowell, applied to trademark "Rhythmix" in Europe, despite being "fully aware" that it was already trademarked as a charity for vulnerable young people.
"Rather than seeking any discussion with the charity, considering any of the moral implications of their actions, or checking with the charity whether the pursuit of an exclusive trademark might have a negative impact on the activities of the charity, Simco and their legal representatives apparently sought a way to use the law to circumvent the trademark of the charity," Davyd said.
"We don't buy this media invention of you as Mr Nasty. Your Wikipedia entry explains at length your involvement with children's charities, and we commend you for it. But equally we don't believe that you are unaware of the way your own company is acting. Or maybe your staff are trying to 'manage' it for you?"
Davyd added that the charity, which has worked with over 40,000 people in the last 12 years, is being forced to take legal action to ensure its continued existence in light of Simco's action.
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"Maybe those young people won't be on your programmes, or your record label, but the music they create is important to them," he said.
Davyd concluded: "A large number of the public reading this will see it for exactly what it is; a ridiculously overblown storm in a tiny teacup. Simco are solely responsible for that situation and you can resolve it in a matter of seconds.
"For that reason, Simon, we are personally asking you to sort this problem out in the quickest and simplest way: Just change the name."