A business card handed to the Labour party appears to suggest Mr Greensill had a UK Government phone number as well as a Downing Street email address.
The UK Government had previously claimed Mr Greensill's role was unpaid and approved "in the normal manner”.
It is alleged the Australian financier was given access to the departments while Mr Cameron was in No.10 so Mr Greensill could promote a financial product he specialised in.
The failure of Greensill, a financial services company, has left many fearing that thousands of jobs at Liberty Steel’s assets in the UK could be at risk, including those who work at the Lochaber aluminium smelting plant in Scotland.
Now the Labour party has demanded a full investigation.
Shadow chancellor Anneliese Dodds said: “This raises further serious questions about the special access Lex Greensill was granted to the heart of government.
“The public have a right to know what happened here – we need a full, transparent and thorough investigation.”
A watchdog said last week that Mr Cameron did not break his own lobbying rules in trying to secure government help for the firm.
It comes as Chancellor Rishi Sunak was accused of breaking the ministerial code for failing to declare Mr Cameron’s approaches.
Tom Brake, a former Liberal Democrat MP who helped design the lobbying register, claimed the Chancellor was required to publicly declare any unplanned discussions with lobbyists such as Mr Cameron, who joined Greensill as an adviser in 2018.
He explained: “The ministerial code is clear.
"Attempts to lobby Rishi Sunak, even an informal one such as receiving multiple text messages, a) must be reported back by Mr Sunak to the Treasury; and b) the contact must then be formally reported in Mr Sunak’s quarterly report of ministerial meetings.
“It is not clear whether the first happened. The second did not. This is a significant breach by the Chancellor of the ministerial code and the transparency rules”.
A UK 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."