There are already “some quite robust systems” in place on lobbying, a senior minister has argued in the wake of the Greensill Capital controversy.

A series of probes have been commissioned, including by Downing Street, as Westminster looks to understand the role former prime minister David Cameron played in securing Whitehall access for Greensill, which was selected as an intermediary lender for some Government Covid-19 support loans at the start of the pandemic, and whose collapse now risks thousands of jobs, particularly in the steel sector.

The saga deepened last week after it emerged the former head of government procurement, Bill Crothers, took a part-time position with the failed firm while still in his Whitehall post.

What I am saying is that we have already got some quite robust systems in place

But while Environment Secretary George Eustice said there might be “tweaks” required following the review into Greensill by No 10, the Cabinet Secretary and parliamentary committees, he argued the system is already “pretty good”.

Mr Eustice, who also defended Mr Cameron’s actions, told the BBC’s Andrew Marr Show: “What I am saying is that we have already got some quite robust systems in place and the principal one is the ministerial code – it is about how ministers conduct themselves based on the people they have talked to.

“So, we should be worried less about who they have talked to, worried much more about ‘are they unduly influenced by individuals?’

“And that is why they declare meetings they have, that is why they declare financial interests, it is why they declare any other potential interests of family members – and that does happen and we all do that.”

But Labour accused the Government of failing to understand the extent of the controversy if ministers thought only “tweaks” were required to the current lobbying rules.

Shadow chancellor of the Duchy of Lancaster Rachel Reeves said: “Having failed to deflect the blame, the Government’s latest approach appears to be to shrug their shoulders and say, ‘Scandal? What scandal?’.

“We don’t need the ‘tweaks’ Eustice said they might consider today, we need to tackle Tory sleaze with a full, independent, transparent inquiry – and we need stronger measures to put integrity and honour back into heart of Government.”

Meanwhile, the Liberal Democrats joined Labour in urging for reform of transparency rules, with leader Sir Ed Davey calling it “wrong” that the Prime Minister is “judge and jury” when it comes to deciding if the ministerial code has been breached.

The controversy over the relationship between Government and the private sector follows disclosures that Mr Cameron personally lobbied Chancellor Rishi Sunak on Greensill’s behalf and was able to arrange for its founder, Lex Greensill, to have a “private drink” with Health Secretary Matt Hancock.

The Sunday Times also reported that Mr Cameron used a former Cabinet Office contact who has since moved onto a senior NHS position to secure a lucrative health contract, allowing Greensill to roll out its advance payment app, Earnd, to doctors and nurses.

Mr Cameron has admitted to pressing the Treasury for Government support for Greensill before its collapse but he “didn’t get anything for it”, Mr Eustice said.

Mr Eustice said the Chancellor had “not acted at all improperly” and that Mr Cameron had “not broken any of the rules”.

The Cabinet minister, who served as press secretary to Mr Cameron when he was leader of the opposition, told Andrew Marr the former prime minister could not be “begrudged” for taking up a new career five years after leaving government.

“He himself conceded that, with hindsight, he should have written it in a more formal way in a letter through the private office,” he added.

“But the real question here is what did the Chancellor do when he was contacted?

“Well, he flagged the conversation with his officials, he asked them to look at it, the answer came back that ‘No, nothing can be done’ and the company (Greensill) didn’t fit the criteria.

“The company was told, ‘we’re not going to help you’, and it went bust, so basically nothing changed.”

With a by-election in Hartlepool and local elections looming next month, the Prime Minister has been warned by a Conservative grandee that he risks losing his gains in Labour’s heartlands, which gave him his 2019 majority, if he does not clean up the “shameful” Westminster lobbying controversy.

Sir Bernard Jenkin, chair of the Commons Liaison Committee – made up of senior MPs, wrote in The Observer that a failure to be “more transparent” than previous administrations could see the so-called “red wall” seats turn away from the Tories.

Asked about Sir Bernard’s criticisms, Mr Eustice said the issue “absolutely does matter to the Prime Minister” and that he had established a review, being led by lawyer Nigel Boardman, into what went on with Greensill.

“We need to let that review take its course and then we can take a judgment on whether there needs to be any change,” he said.