Boris Johnson has ordered an independent investigation into David Cameron’s controversial lobbying of ministers for the collapsed financier Lex Greensill.

A leading lawyer will probe “how business representatives engaged with government” in discussions over supply chain finance and how contracts were awarded, No 10 said.

The move comes amid a storm of criticism of the former prime minister after he directly lobbied Rishi Sunak, including by text, to give Greensill a role in the government’s Covid-19 loan scheme.

At the weekend it emerged he had also organised a “private drink” with the health secretary Matt Hancock, with at least four ministers contacted.

Downing Street said Mr Johnson had launched the independent review because he recognised the “significant interest” in the controversy.

“The prime minister has called for the review to ensure government is completely transparent about such activities and that the public can see for themselves if good value was secured for taxpayers’ money,” his spokesman said.

“This independent review will also look at how contracts were secured and how business representatives engaged with government.”

The inquiry will be led by Nigel Boardman, an award-winning lawyer who is also a non-executive board member at the business department – a post he is expected to leave.

No 10 promised he would have “access to the documents that he needs’, but was unable to say if he would have legal powers to secure evidence or be able to recommend changes to lobbying rules.

In further unanswered questions, it was also unclear whether the inquiry would include the behaviour of ministers and whether there had been any breaches of the ministerial code.

No 10 declined to say whether Mr Johnson supported a toughening of the rules, arguing it did not want to “close off avenues while Mr Boardman is starting his work”.

Labour was quick to attack an investigation which “has all the hallmarks of another cover-up by the Conservatives”.

“Just as with the inquiry into Priti Patel’s alleged bullying, this is another Conservative government attempt to push bad behaviour into the long grass and hope the British public forgets,” said Rachel Reeves, the shadow Chancellor of the Duchy of Lancaster.

“We need answers on Greensill now – that means key players in this cronyism scandal like David Cameron, Rishi Sunak and Matt Hancock appearing openly in front of Parliament as soon as possible to answer questions.”

Earlier, another former prime minister, Gordon Brown, said those in his position “must never” lobby government for commercial purposes and suggested those leaving No 10 should be subject to at least a five-year ban.

Mr Cameron has conceded it was a mistake to lobby ministers informally on behalf of Greensill, but has insisted he did not break any rules.

He also said the value of his shares in Greensill’s collapsed company was “nowhere near” the figure of up to $60 million that had been reported.

Mr Cameron insisted he had “very little to do” with Greensill while in No 10 and met him only twice when prime minister, despite the financier describing himself as a “senior adviser”.

Official records released by the Treasury last week showed that Mr Sunak responded to Mr Cameron by saying he had “pushed” civil servants to explore possible options.

Mr Cameron was lobbying for the supply-chain finance company to be allowed to access the Bank of England’s Covid Corporate Financing Facility.

The Sunday Times revealed that Mr Cameron had emailed a senior special adviser to Mr Johnson to complain that it was “nuts” that Greensill had been excluded and urging the government to reconsider.