Dacre should not be within a million miles of any regulatory function of the press.
As far as the media goes, self-regulation is not working. It does not provide sufficient redress for those harmed by a story which wrecks their reputations- rather like Chris Jeffries over the Bristol murders episode. People rarely get a right of reply, and when they do, the paper in question often hides it away, or ,like with Miliband, use it as an opportunity to simply repeat the baseless allegations that prompted the request for a right of reply in the first place.
Some change is long overdue, since the Press have shown themselves incapable of restraint, repeatedly crossing the line when publishing stories.
A regulatory framework truly independent of the Press and with the power to enforce and direct things like where the paper must publish a prominent apology, for instance, or a right of reply, or that can act as a arbitrator to assign damages payments etc is necessary.
The press whine that with greater regulation, they will be handcuffed, muzzled, unable to report on contentious stories for fear of the regulator, but that is complete rubbish; Papers will always have the public interest defence where appropriate.