Video report by ITV News Political Correspondent Libby Wiener
Mounting an attack on Boris Johnson at PMQs, the Labour leader said the "whole broken system" of lobbying needs an overhaul, saying recent claims against the government amount to the "the return of Tory sleaze".
The PM said an inquiry led by lawyer Nigel Boardman would examine the situation after it emerged the Government's former procurement chief had worked for Greensill Capital while still employed as a civil servant.
Meanwhile senior Tory William Wragg said Mr Cameron's lobbying for the collapsed lender was "tasteless, slapdash and unbecoming" and indicated his cross-party Public Administration and Constitutional Affairs Committee could investigate the row.
The Treasury Select Committee will also examine the regulatory lessons from the collapse of Greensill and Chancellor Rishi Sunak's department's response to lobbying by Mr Cameron.
The prime minister said he shares some of the widespread concern about how former PM Mr Cameron was lobbying ministers on behalf of collapsed finance firm Greensill Capital.
He said after reading reports this week that it is not clear whether the "boundaries" between civil servants and business had been "properly understood".
But Mr Johnson would not commit to an independent parliamentary inquiry, saying the Cabinet Office-commissioned inquiry he had ordered by Mr Boardman would find answers.
Mr Cameron intends to respond “positively” to any request to give evidence to any of the inquiries taking place into the Greensill affair, a spokesman for the former prime minister has said.
Following the announcement that the Commons Treasury Committee is to hold an inquiry into the firm’s collapse, the spokesman said Mr Cameron was keen that “lessons are learned”.“David Cameron will respond positively to all such requests when the terms of reference of each inquiry are made clear and any invitations to provide evidence are received,” the spokesman said.“While he was an adviser to the business and not a board director, he is keen to ensure that lessons from it going into administration are learned.”
Sir Keir said: "The prime minister says there's going to be an inquiry but the person he's appointed worked for the law firm which lobbied to loosen lobbying laws. You couldn't make it up."
He accused the PM of blocking a proper inquiry, adding: "The Greensill scandal is just the tip of the iceberg. Dodgy contracts, privileged access, jobs for their mates, this is the return of Tory sleaze.
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"It's now so ingrained in this Conservative Government, we don't need another Conservative Party appointee marking their own homework.
"The more I listen to the Prime Minister, the more I think Ted Hastings and AC-12 is needed to get to the bottom of this one.
"We know the Prime Minister will not act against sleaze, but this House can."
Despite Sir Keir's pleas that it was time to "clean up the sleaze and cronyism that's at the heart of this Conservative Government", Labour lost a vote on whether to set up a parliamentary inquiry, by 105 votes.
Mr Johnson insisted the government has been "tough" on lobbying, adding: "We're getting on with rooting out bent coppers. We're also appointing and hiring thousands more police officers and fighting crime on the streets of our cities while they oppose the police and crime Bill."
Mr Wragg said the Public Administration and Constitutional Affairs Committee, which he chairs, will be investigating the lobbying scandal.
"I have full confidence in the members of the committee to discharge their duties and do not require a re-organisation."
He added: "I would ask the House to be assured that we will pursue every possible line of inquiry with our witnesses and shall conduct ourselves without fear or favour."
He too made a Line of Duty reference during his remarks, saying he'd be "more than happy to take up as the AC-12 of Whitehall".