This perspective is not entirely unfamiliar or unwelcome in America; it reigns on many of our college and university campuses that severely restrict student speech. So while an American politician might hesitate to issue a forthright call for an inquiry into press ethics and culture, significant segments of the American public might favor one (for different segments of the press for different reasons). If the News of the World hacking scandal is a morality play about renegade journalists, the official response to it is cautionary tale about subtler forms of press censorship.
Cameron's July 8th speech addressing the scandal included the obligatory concession to a free press, accompanied by the contrary assertion that the press should not be free to police itself. Acknowledging that it should not be policed by government, Cameron imagined some lofty, "truly independent" oversight group comprising a "credible panel of figures ... from different backgrounds" that would hold the press to "proper standards of decency." You may have to listen to his speech to appreciate its priggishness and the delusional elitism underlying the assumption that a small collection of professionally "credible" overseers could identify objective, widely held standards of decency and impose them on the press without infringing on its essential freedoms.
In part, this assumption reflects the belief that the tabloid press--the primary object of outrage--can be distinguished from the respectable press. Indeed, you can find (short-sighted) support in the respectable press for Cameron's vision of right thinking regulators: "Standards of taste, decency and practice are not difficult to form. Calibrating them is often trickier, but far from impossible," a column in the respectable Guardian declares, effectively endorsing the Prime Minister's call for press regulation. "We need a free press that is also clean and trustworthy," Cameron announced, like a latter-day Anthony Comstock; "that is what the people want, that is what I want and I will not rest until we get it."
But if the people wanted a "clean" press they probably wouldn't consume one devoted to exposing and exaggerating dirt about major and minor celebrities. They wouldn't be swayed by the tabloids' schoolyard attacks on politicians (and politicians wouldn't be cowed by the tabloids). I'm not questioning genuine public outrage over alleged phone hacking targeting families of murder or terror victims and soldiers; but if the public were generally outraged by the "culture" of the tabloid press they would simply stop reading it. The attack on press culture is in part an attack on the preferences of its readers.
What "the people" seem more likely to want and what the government has legitimate power to provide, is not a presumptively "clean" or "decent" press but a non-criminal one, (or, at least, one that only engages in criminal conduct when it targets celebrities and politicians.) The press is not above the law, as Cameron declared; publishers and journalists engaged in criminal activity should be prosecuted, along with any police officers and politicians who abetted them. But press culture is outside the law, and inquiring into it distracts from investigations of alleged criminal activity, involving police as well as journalists.