Bill Crothers's part-time position had been "agreed" to by the Cabinet Office, the Office of the Advisory Committee on Business Appointments added.

Its chairman Lord Pickles complained of a "lack of transparency" over the situation.

But Mr Crothers said he had been taken on by Greensill in a "transparent" way.

Labour called his dual employment "extraordinary and shocking".

The disclosure about Mr Crothers - who had been the government's chief procurement officer prior to being taken on by Greensill - is the latest of several stories involving the now-collapsed financial firm.

It employed former prime minister David Cameron as an adviser from 2018. The Financial Times and the Sunday Times revealed that he had contacted several ministers, including Chancellor Rishi Sunak, to push for greater involvement in government loans schemes for the company.

Boris Johnson has set up an inquiry into lobbying - attempts to persuade governments to change policy - including Greensill's role.

Government sources said this would also now look at the situation surrounding Mr Crothers.

Mr Crothers, who had already left his job as chief procurement officer but remained a Civil Service employee, joined Greensill as an adviser to its board in September 2015.

The letter from Conservative peer Lord Pickles to leading civil servant Alex Chisholm says: "This was agreed by the Cabinet Office under its internal conflicts-of-interest policy."

Lord Pickles asks for "guidance on the conflicts-of-interest process" undertaken.

The letter adds: "The lack of transparency around this part-time employment with Greensill may have left the misleading impression that Mr Crothers had wilfully ignored the obligation to seek advice."

Mr Crothers left the Civil Service in November 2015, two months after taking up his role at Greensill. He became a director of the firm in late 2016.

'Transparent'

A letter from Mr Crothers to Lord Pickles, a former Conservative Party chairman, written earlier this week, has also been published.

In it, he says: "I am concerned that there may be a view that I did not follow proper process regarding my role with Greensill Capital.

"I assure you that I completely respect the required process and your office, took steps to comply, and believe that I did so."

He adds: "I was transparent about the move to Greensill Capital, and it was well known at the time."

For Labour, shadow Cabinet Office minister Rachel Reeves said: "This is an extraordinary and shocking revelation.

"The Conservatives have weakened the rules so much they may as well rip them up and start again."

The inquiry into lobbying is expected to report its findings by the end of June.

A Cabinet Office spokesperson said there would be a response to Mr Pickles's letter "in due course".

They added that the "review into Greensill Capital and supply-chain finance" would be "wide-ranging".

Mr Cameron has said he did not break any codes of conduct or rules on lobbying and that he welcomes the investigation launched by Mr Johnson.