According to the survey by Yougov, 49pc favour the model which is used by to fund the Independent Press Standards Organisation, compared to just 4pc who think a watchdog should be funded by donations from wealthy individuals and trusts.
The same poll, commissioned by newspaper industry body the News Media Association, also found that just 1pc of respondents thought press regulation should be among the top four priorities.
Of those polled, 68pc also believe that news on social media platforms like Facebook, which are currently unregulated, should be subject at least to the same level of regulation as newspapers or even tighter regulation.
Lynne Anderson, News Media Association deputy chief executive, said: “This survey demonstrates conclusively that a regulatory regime led by Impress – which is completely reliant upon funding from one wealthy individual, Max Mosley – cannot command the confidence of the public.
“IPSO is funded in its entirety by its member national, regional and local newspaper publishers which is the funding model the public want and expect from an industry which is committed to robust self-regulation.
“It is also abundantly clear from the poll that there is absolutely no public appetite for further activity from the Government in this area – such as the reopening of the Leveson Inquiry – when there are other much more pressing priorities at hand.”