Labour has ramped up calls for an inquiry into the Government’s links with Greensill Capital following reports that the former head of Whitehall procurement took a job with the firm without proper vetting.

Bill Crothers joined the board of the financial firm in 2016, less than a year after leaving his post as the government’s chief procurement officer, according to reports in The Times and Financial Times.

According to the papers, he failed to obtain permission from the official advisory committee on business appointments (Acoba) which is supposed to vet any private sector appointments taken by former ministers and senior servants within two years of leaving their posts.

Two years later, in 2018, Greensill – founded by the Australian financier Lex Greensill – was involved in running a contract won by the US software firm Taulia to provide “supply chain finance” to NHS pharmacies.

The Government has already been facing questions over David Cameron’s links with Greensill when he was prime minister and subsequent lobbying on its behalf after he left office.

The firm has since filed for insolvency after failing to secure support through the Government’s Covid Corporate Financing Facility. Its collapse threatens thousands of jobs in Liberty Steel.

In a letter to the Cabinet Secretary Simon Case, shadow chancellor Anneliese Dodds and shadow cabinet office minister Rachel Reeves called for a “full, transparent and thorough investigation” into Greensill’s links with the Conservative government.

“The irresponsible behaviour of Greensill Capital and its almost unparalleled access to the heart of Government raises serious questions about what kind of businesses the Government is engaging with,” they said.

A Cabinet Office spokesperson said: “We will respond to the letter in due course.”

The latest claims came after Labour said it had been handed a business card dating from Mr Greensill’s time working as an adviser in the Cabinet Office, describing him as a senior adviser in the prime minister’s office.

The card, which was said to have been given to an industry figure in 2012 shortly after Mr Greensill became an unpaid adviser on supply chain finance issues, included a Downing Street telephone number and email address.

After he left office, Mr Cameron became an adviser to Greensill Capital, and reportedly personally lobbied Chancellor Rishi Sunak for cash support for the firm through the Covid Corporate Financing Facility.

He took the job two years after leaving No 10 and therefore it did not require the approval of Acoba.

Asked about Mr Cameron’s approach, Mr Sunak told ITV News: “I think it’s important that, whoever people are, whether they’re prime ministers or anyone else, that they follow the rules and the guidelines that we have in place for lobbying.

“We have the rules in place for good reason. And I think whoever you are, it’s important processes are appropriately followed.”

Earlier, in response to questions about Mr Cameron’s links with Greensill, Communities Secretary Robert Jenrick said former ministers should conduct themselves with care.

“You have to be careful to uphold standards in public life,” he told BBC News.

“You do have to be very careful how you conduct yourself once you leave office and not to use any of the privileged information or contacts that you might have in a way which does harm to your office or to public life more generally.”

Labour leader Sir Keir Starmer repeated his calls for an inquiry, saying the former prime minister should “come out of hiding” and explain his links with Greensill.

“Every day this gets more murky and cronyism is the only real word now for what we’re seeing. I think in light of the latest developments, it’s time for that inquiry,” he told reporters during a visit to Leeds.

“I think the Cabinet Secretary needs to look at this again in the round and I also think it’s time for David Cameron to come out of hiding and start answering some questions.”