Here is what Lord Justice Leveson says on the matter:
There are many forms of statute law which already restrict the activities of the press, whether in terms of their organisation, competition or activities up to and including in limited cases what it may or may not be lawful to publish (race hate, for example).
On the face of it, these statutory restrictions are legitimate and proportionate exercises in democratic lawmaking, balancing competing public freedoms and goods ...
But to contend that no statutory reform could be so is to push the argument far beyond any reasonable statement of principle.
Ultimately, there is no necessary connection between statutory underpinning of a regulatory system ... on the one hand, and state censorship on the other, nor in my view is there some sort of slippery slope gliding from the first to the second.