Mr Cameron, speaking at his monthly press conference, said: "Anyone who watched the Dispatches programme last night could not help but be, frankly, disgusted by what they saw.
He added: "We need a proper [government] inquiry into all of this."
Chairman of the committee on standards in public life, Sir Christopher Kelly, said he had been "greatly saddened" by the Dispatches programme and "the further damage that will do to people's perception of members of Parliament".
He said rules banning paid-for advocacy in the Commons were "quite clear" and what was required was "proper enforcement and proper sanctions when misbehaviour occurs".
"In all of this what's really required is changes in behaviour, it requires a culture in which the principles of public life, selflessness, integrity and so on, are embedded in the behaviour of those who hold public office."
Three other politicians were featured in the programme - Labour MP Margaret Moran, Labour's Baroness Sally Morgan and Conservative MP John Butterfill.
'Cab for hire'
It is understood that Mr Butterfill has referred himself to the standards commissioner and Baroness Morgan has already referred herself to the sub-committee on Lords' interests.
Ms Moran, already deselected by Labour as an election candidate following revelations over her expenses, has been suspended by the Parliamentary Labour Party.
Under Commons rules MPs can work for companies, but must declare payments and may not lobby ministers directly.
Mr Byers, a former transport secretary, was filmed saying he was like a "cab for hire" who would work for up to £5,000 a day and claimed to have saved millions of pounds for National Express, which wanted to get out of its East Coast mainline franchise.
More clips from Channel 4's Dispatches programme
Transport Secretary Lord Adonis told peers on Monday there was "no truth" in claims he came to "any arrangement", dismissing the comments as "pure fantasy".
Mr Byers also said he had spoken to Business Secretary Lord Mandelson about getting food labelling proposals delayed, on behalf of supermarket Tesco.
The business department, Tesco and National Express denied the claims - and Mr Byers said later he had overstated his case and had never lobbied ministers.
Lord Mandelson told the BBC had had no contact with Mr Byers about food labelling and said it was "rather grubby" that the MP had made "completely untrue, unfounded boasts... in order to get himself future business".
Former Defence Secretary Mr Hoon was filmed by Dispatches saying he wanted to make use of his international knowledge and contacts in a way that "makes money" and that he charged £3,000 a day.
Mr Hoon has said he had made clear that he would not lobby government or "attempt to sell confidential or privileged information arising from my time in government".
Ms Hewitt, a former health secretary, said she "completely rejected" the suggestion she helped obtain a key seat on a government advisory group for a client paying her £3,000 a day.
BBC political editor Nick Robinson said the three former ministers were not popular among Mr Brown's team - Mr Hoon and Ms Hewitt tried to lead a coup against his leadership in January. All three are due to stand down as MPs at the next election.
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