A review is expected to be launched into Greensill Capital, the collapsed financial firm for which David Cameron lobbied ministers.

The former prime minister has accepted he should have communicated with the Government “through only the most formal of channels” rather than text messages to chancellor Rishi Sunak as he acknowledged mis-steps over the controversy.

Greensill collapsed into administration in March.

Breaking his weeks of silence, the former Conservative prime minister said in a statement to the PA news agency that having “reflected on this at length” he accepts there are “important lessons to be learnt”.

No 10 sources confirmed a review will be launched into Greensill, although details of the investigation have not yet been released.

But Labour said his attempt to draw a line under the issue on Sunday evening leaves “many serious questions” unanswered and demanded he addresses them before Parliament.

Former Labour leader Mr Brown said that former prime ministers should not be “lobbying for commercial purposes” and suggested legislation banning the practice for five years if existing rules cannot be made to work.

“I can’t comment on the individual detail of this but for me there are principles about public service – it cannot ever become a platform for private gain,” the former prime minister told BBC Radio 4’s Today programme.

“Ministers must never be lobbying, former ministers, prime ministers, must never be lobbying for commercial purposes. Current ministers should not be entertaining such lobbying.

“If we can’t succeed in achieving this stopping by the sort of flexibility of the rules, we are going to have to pass laws to make sure that at least for, say, five years, no serving or former prime minister or minister is ever lobbying for any commercial purpose within government.

“It simply brings public service into disrepute.”

The row surfaced when it emerged Mr Cameron privately lobbied ministers, including with texts to Chancellor Rishi Sunak, to win access to an emergency coronavirus loan scheme for his employer, financier Lex Greensill.

It was later reported Mr Cameron had arranged a “private drink” between Health Secretary Matt Hancock and Mr Greensill to discuss a payment scheme later rolled out in the NHS.

The former prime minister – who was in Downing Street from 2010 to 2016 – said in a statement: “In my representations to Government, I was breaking no codes of conduct and no government rules.”

He said that “ultimately” the outcome of his efforts to get Greensill’s proposals included in the Government’s Covid Corporate Financing Facility (CCFF) was that “they were not taken up”.

“So, I complied with the rules and my interventions did not lead to a change in the Government’s approach to the CCFF,” he added.

“However, I have reflected on this at length. There are important lessons to be learnt.

“As a former prime minister, I accept that communications with government need to be done through only the most formal of channels, so there can be no room for misinterpretation.”

Questions had been mounting over his efforts to secure access for the finance company, which later collapsed, putting thousands of UK steelmaking jobs at risk.

Mr Cameron said that “many of the allegations” made in recent weeks “are not correct” as he challenged what he said is was a “false impression” that Mr Greensill was a key member of his team while in No 10.

It comes after it emerged the Chancellor responded to the numerous private texts from Mr Cameron by saying on April 23 last year that he had “pushed” officials to consider plans that could have helped Greensill.

Mr Cameron also described the decision to exclude his employer’s firm from the multibillion-pound scheme as “nuts” in an email to a senior adviser to Prime Minister Boris Johnson and pressed for the Chancellor to reconsider.

“What we need is for Rishi (Sunak) to have a good look at this and ask officials to find a way of making it work,” Mr Cameron emailed on April 3 last year.

Labour called for Mr Sunak to “come out of hiding” and make a statement to Parliament about the “growing scandal”, and reiterated demands for an investigation.

As Mr Cameron pointed out, the Registrar of Consultant Lobbyists cleared him of breaking lobbying rules because as an employee of Greensill he was not required to declare himself on the register.

Labour’s shadow chancellor of the Duchy of Lancaster Rachel Reeves said: “Many serious questions remain unanswered and it is crucial that the former prime minister appears before Parliament so that all the information is brought to light.

“Transparency and accountability are crucial and that requires the utmost openness from government to establish the full facts behind this scandal.”