Former ministers like David Cameron need to be “very careful” how they conduct themselves, the Communities Secretary has said, amid growing controversy over the ex-premier’s lobbying activities.

Robert Jenrick said it was important that those who had had the “privilege” of serving in Government did not act in a way which “does harm” to the office they held or to public life more generally.

His comments came as Labour continued to press for an inquiry into Mr Cameron’s links with the Australian financier, Lex Greensill.

The party said that 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 Greenhill 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 Mr Greensill’s company, Greensill Capital, and reportedly personally lobbied Chancellor Rishi Sunak for cash support for the firm through the Government’s Covid Corporate Financing Facility.

The company was subsequently filed for insolvency after its application for support was rejected by officials.

Business Secretary Kwasi Kwarteng has previously said that Mr Cameron had only started working for Greensill Capital two years after leaving office, in line with the rules for former ministers.

Mr Cameron has made no public comment on the reports.

In response to questions about Mr Cameron’s links with Greensill, Mr 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.”

Mr Jenrick said that he could not comment directly on Mr Cameron’s activities, adding: “I don’t know the details, that is really a question for him.”

He said however that it was normal for ministers to bring in unpaid advisers like Mr Greensill to work on specific issues.

“What I understand happened is that he acted as an unpaid adviser to the then-Government on a particular issue around financing supply chains,” he said.

“There are unpaid advisers to Government. They have to go through certain processes advised by the Civil Service. Beyond that I don’t know what happened at that time. That was obviously a previous Government.”

He added: “If he had a business card or an email address, it will have been, I imagine, signed off by civil servants at the time.”

Labour leader, Sir Keir Starmer, repeated 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.”