The government will examine suggestions to improve lobbying rules after a series of inquiries, the environment secretary has pledged.
George Eustice said current systems were "quite robust" but it was possible they could be "tweaked or improved".
He said David Cameron's actions were "acceptable" when he lobbied ministers on behalf of finance firm Greensill Capital.
But Labour said the row over the ex-PM's work had eroded trust in politics.
A government review and three separate MP-led inquiries are now looking into Mr Cameron's attempts to lobby ministers on behalf of Greensill.
His work for the firm, which collapsed in March, has prompted increased scrutiny of private companies' attempts to influence ministers and officials.
Mr Cameron began working as an adviser to Greensill in August 2018, just over two years after he stood down as PM in July 2016.
He has been criticised for unsuccessfully trying to help the firm, in which he had a financial interest, gain access to government-backed Covid schemes, including by sending text messages to Chancellor Rishi Sunak.
He also met Health Secretary Matt Hancock in 2019 for a "private drink" to discuss a new payment scheme for NHS staff developed by the firm.
Currently, former ministers are not allowed to lobby government for two years after they leave office - a rule the ex-PM appears to have followed.
But critics of the current system, including former Labour prime minister Gordon Brown, have suggested a longer ban is required.
All external lobbyists also have to list their work on a special register - although as an in-house employee, Mr Cameron was not required to do this.
Asked whether Mr Cameron's work for the firm was acceptable, Mr Eustice told the BBC's Andrew Marr show: "Well it is acceptable obviously, because he would have worked within the rules."
Mr Eustice said that all current cabinet ministers will be asked to declare contact with the firm as part of the government review, to be led by lawyer Nigel Boardman.
"Once it's concluded, and once all those parliamentary committees that are now looking at this have concluded, I'm sure some of them will make policy recommendations.
"And of course the government will look at that. I'm not saying that things couldn't be tweaked or improved."
The terms of reference for the government's own review say Mr Boardman will report "findings and any recommendations" to Prime Minister Boris Johnson by the end of June.
Speaking earlier to Sky's Sophy Ridge, Mr Eustice said that review was "not really there to prescribe policy" and would not have enforcement powers.
What is lobbying?
- It's another word for trying to persuade the government to change its policies
- It can be done by individuals, companies, organisations and charities who contact ministers, backbench MPs and other politicians
- Some organisations and companies employ professional lobbyists to make their case for them
- Former MPs and civil servants often work as lobbyists
Labour's shadow Cabinet Office minister Rachel Reeves said the Greensill affair showed the need for stricter lobbying rules.
She told the Marr programme that the Advisory Committee on Business Appointments (Acoba), which advises former ministers and civil servants on outside employment, should be given greater powers.
"We are seeing the erosion of trust in our politics because of the behaviour by a few at the top of the Conservative Party," she added.
Liberal Democrat leader Sir Ed Davey, who was energy secretary under Mr Cameron during the Tory-Lib Dem coalition government, said "much greater transparency" over lobbying was required.
He suggested the code which governs the behaviour of current ministers should be overseen by an "independent body" similar to the one that oversees MPs' expenses.
Meanwhile, senior Tory MP Sir Bernard Jenkin has warned Mr Johnson he could lose trust from former Labour voters in "red wall" constituencies they won in the last election - unless he can show he is more transparent.
Writing in the Observer newspaper, Sir Bernard said the current system had "allowed the lines between public service and private gain to become blurred".
He said there had been a "failure of successive governments" to be more transparent about the relationships between administrations and business.
Mr Cameron has defended his work for Greensill but accepted he should have contacted ministers using more formal channels.
He has said he welcomes the government review and will "respond positively" to any requests from MPs for him to give evidence.
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