A scandal-hit financier claimed he was a "senior adviser" to then prime minister David Cameron, according to a business card handed to the Labour Party.
The card suggests Lex Greensill had a government landline phone number as well as a Downing Street email address.
The government has previously claimed Mr Greensill's role was approved "in the normal manner", but not paid.
Labour said there are "further serious questions about the special access Lex Greensill was granted to the heart of government" and a "full, transparent and thorough investigation" is needed.
Sky News has approached Mr Cameron and the Conservative Party for comment about the business card.
It comes after a cabinet minister told Sky News it was time to "move on" from the row over Mr Cameron's dealings with Mr Greensill's financial services company.
"I think people have looked at this. As far as I know, David Cameron did absolutely nothing wrong," Business Secretary Kwasi Kwarteng said when asked about the ex-prime minister's links to Greensill Capital.
He added: "People have looked into his role, people looked into the fact that he may or may not have contacted people, officials in the Treasury.
"As far as I know, everything was above board, he's been largely exonerated and I think we should just move on."
A watchdog said last week that Mr Cameron, who was in Downing Street from 2010 to 2016, did not break his own lobbying rules in trying to secure government help for the firm.
As well as seeking funds from a government-backed COVID loans scheme, Mr Cameron is also alleged to have approached the Bank of England about the firm.
Greensill Capital collapsed earlier this month and has left Liberty Steel, along with its 5,000 workers in the UK, facing an uncertain future.
Reports that Mr Cameron sent a number of texts to Chancellor Rishi Sunak's private phone asking for support for Greensill Capital were investigated by Harry Rich, the Registrar of Consultant Lobbyists.
That post was set up in legislation passed by Mr Cameron's own government in 2014.
But, as an employee of Greensill, which has since gone into administration, he was not required to declare himself on the register, Mr Rich concluded.
However, Labour is now calling for the standards watchdog to look into government links to Greensill.
The party wants the Committee on Standards in Public Life to launch an investigation.
"What's happening with Greensill gets murkier by the day and I think it's obvious that there's got to be an inquiry," party leader Sir Keir Starmer said on Tuesday.
"There are too many unanswered questions."
It comes after a Sunday Times investigation alleged that founder Lex Greensill enriched himself through a government-supported loan scheme that he designed after Mr Cameron gave him access to 11 departments and agencies.
The newspaper reported that the Australian financier was given access to departments while Mr Cameron was prime minister so he could promote a financial product he specialised in.
The Pharmacy Early Payment Scheme saw banks quickly pay back pharmacists for providing NHS prescriptions, for a fee, before getting the cash back from the government.
Greensill Capital provided funds for the scheme.
The Sunday Times said Mr Greensill could not be reached for comment, but reported he was understood to deny making large sums from a pharmacy deal.
Sky News has approached Greensill Capital for a comment through its administrators on a number of occasions, but has yet to receive a response.
A government spokesman said: "Lex Greensill acted as a supply chain finance adviser from 2012 to 2015 and as a crown representative for three years from 2013.
"His appointment was approved in the normal manner and he was not paid for either role."
Sky News has approached Mr Cameron's office for a comment since the reports around Greensill Capital emerged, but has not had a response.
Lord Evans, chair of the Committee on Standards in Public Life, said in response to Labour's letter that it is an advisory body and "does not have a remit to investigate individual cases".
However, he added that the committee was currently looking into arrangements surrounding transparency and public appointments and would welcome submissions from the party on the matter.
Giving his take on the row, Sir Alistair Graham, a former chair of the committee, told Sky News: "Mr Cameron, I think, was cleared very much on a technicality of having been an in-house employee rather than an independent lobbyist.
"But he was the one who identified that lobbying was likely to be the next major scandal and here we find him, in effect, lobbying to help Greensill Capital achieve loans from the British government.
"It appears, although I don't know obviously the detail, that also this company had very privileged access to Treasury and government departments in a way I don't think is acceptable."
Sir Alistair added: "I have an unease about what seems to be an expectation by former cabinet ministers, former prime ministers.
"Feeling that it's almost part of their pension arrangements that they should be able to have key positions in the private sector, paid a large amount of money and be able - because they've got passes to the House of Commons - to still have some privileged access to government."