Speaking during prime minister’s questions (PMQs) on Wednesday, the Labour leader told Johnson there was “an open door between his Conservative government and paid lobbyists”.
Johnson has rejected Labour’s demand that a parliamentary inquiry into links between Greensill and the government be set up.
MPs will vote later on Wednesday on the proposal, but without government support it is unlikely to pass.
Cameron has been revealed to have lobbied ministers on behalf of Greensill Capital, after he left office, in a failed attempt to secure the firm access to a government loan scheme.
The former PM is reported to have been in line to make millions of pounds as a result of owning shares in the company had his efforts been successful.
But Greensill filed for insolvency after being unable to secure support through the government’s Covid corporate financing facility. Its collapse threatens thousands of jobs in Liberty Steel.
The row deepened on Tuesday after it emerged that a former head of Whitehall procurement had become an adviser to Greensill while still working as a civil servant.
Bill Crothers began working for the firm as a part-time adviser to the board in September 2015 and did not leave his role as government chief commercial officer until November that year.
Starmer said: “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.
“We know the prime minister will not act against sleaze, but this House can.”
During PMQs, Johnson admitted it was “not clear” from the accounts he had read of the Crothers case whether the “boundaries” between Whitehall and business had been “properly understood”.
He added he could not “remember” when he last spoke to “Dave” – as he called Cameron – but denied having had “any contact” with the former PM about Greensill.
Johnson has launched an independent review of Cameron’s lobbying, but Labour has said it will be nothing more than a “Conservative Party appointee marking their own homework”.
City lawyer Nigel Boardman will lead the probe into links between the company and ministers, including personal approaches made by the former PM.