A petition, launched by Hacked Off, the group started by people affected by phone hacking, was initiated last week.
Yesterday, the figure of those in favour of implementing the full Leveson Report had reached more than 110,000 online.
“The public is firmly behind effective, independent regulation of the press,” explained Hacked Off group director Brian Cathcart to the Independent.
However, others fear that some of the less-publicised recommendations in the report could impede investigative journalism.
Prime Minister, David Cameron, last Thursday, voiced his concerns about the proposal of the Leveson inquiry. This has angered Hacked Off members such as Hugh Grant, who explained that it was “very close to disgraceful”.
There are fears that restricting informal meetings between the press and police could suppress whistleblower features. It would also be almost impossible to protect sources.