Cornwall’s new unitary implementation executive unveiled the flame-like logo in June but opponents claim it fails to capture the county’s historical identity.
Senior councillors set up one petition while a another petition against the logo supported by council leader David Whalley (Lib Dem) has been placed on the 10 Downing Street website.
Organiser, county councillor Julian German (ind), told the paper: "The more people who sign, the stronger the message it sends to the decision-makers. Politicians have to start listening to the people.
"This 'we know better' mentality, nurtured by David Whalley, has to be vigorously challenged and we have no intention of giving up this campaign until this universally disliked and unprofessional logo is scrapped."
The Downing Street petition claims the logo “is not an identifiable symbol for Cornwall”.
It says of the logo: “It fails to reflect Cornwall's unique heritage and distinctive culture. We urge the prime minster to listen to the people of Cornwall who wish to retain the internationally recognised and respected traditional Cornish emblem.”