A petition calling on David Cameron to "Save CBeebies and CBBC" was launched after details of John Whittingdale's plans for the future of the BBC were made public.
It was signed by more than 150,000 people before the White Paper was published on Thursday 12 May.
The petition states: "Our children deserve quality television on channels without adverts.
"CBeebies and CBBC allow us those precious few minutes to make a cuppa or put the washing on the line. And it means we don’t have to sit our little ones in front of adverts running every few minutes on the other channels.
"There's something really special about CBeebies and CBBC."
Whittingdale's White Paper on the future of the BBC states that the licence fee is paid by the general public to watch all television channels - not just the BBC.
"While almost all the licence fee income is currently provided to the BBC, that has not always been the case," it reads. "Indeed 12% was used for other purposes prior to 1962."
Whittingdale plans to make "a small proportion" of the licence fee - £20million a year - available to organisations other than the BBC to produce television programmes.
The aim is to end the BBC's "near-monopoly" on children's programming and boost competition between other free-at-the-point-of-use channels, - such as ITV, Channel 4 and Channel 5, - to ensure the audience gets "the best value for money".
The 38 Degree petition's founders fear this will "put the CBBC service and its programmes at risk".
Nat Whalley, campaigns manager at 38 Degrees, said: “We’ve come together in our hundreds of thousands to say to the government: leave BBC children’s programming alone.
"The government will put itself at odds with voters of all political persuasions if it tries to cut CBeebies and CBBC. It can expect a huge backlash from parents and grandparents across the country.”