Labour has called on a standards watchdog to investigate the extent of government access offered to financial services firm Greensill Capital.
The party wants the Committee on Standards in Public Life to examine the role played by the firm's founder in David Cameron's coalition government.
The Sunday Times claimed Lex Greensill had been given "privileged access" to Whitehall departments under the ex-PM.
Neither Mr Greensill nor Mr Cameron has commented on the matter.
Labour said the reports raised questions about transparency rules.
Business Secretary Kwasi Kwarteng told BBC Radio 4's Today programme there was "no suggestion" the former prime minister "could not pursue another career after politics".
He added that he did not think Mr Cameron "did anything wrong", but the government was "always reviewing the rules" and "looking at new circumstances... trying to improve the existing rules and improve the system".
In its letter, Labour asked the committee to examine Mr Cameron's reported role in lobbying the government on behalf of the firm after he left office.
It has previously been reported that Mr Cameron, who became an adviser to Greensill in 2018, unsuccessfully tried to increase the specialist bank's involvement in a scheme offering government-backed loans to companies struggling due to the Covid pandemic.
Greensill, which went bust recently, was accredited to supply lending under the government's Coronavirus Large Business Interruption Loan Scheme (CLBILS).
Mr Cameron was cleared this week by a lobbying watchdog, which looked at whether he should have declared himself on the register of consultant lobbyists over work he had done for the firm since leaving Downing Street.
Over the weekend, the Sunday Times reported that Greensill's founder, Lex Greensill, was given access to various government departments during Mr Cameron's time in No 10.
The newspaper said Mr Greensill had been promoting a financial product for pharmacists.
The Pharmacy Early Payment Scheme, announced in 2012, saw banks swiftly reimburse pharmacists for providing NHS prescriptions, for a fee, before recovering the money from the government.
Greensill Capital went on to provide funds for the scheme.
Labour said the reports raised "serious questions about the level of extensive access to ministers and departments he was granted and the role Mr Cameron played in securing it".
In a letter to its chair, independent peer Lord Evans, the party said the Committee on Standards in Public Life should ask why Mr Greensill's role promoting the scheme had not been "announced internally or publicly".
Shadow chancellor Anneliese Dodds, who co-wrote Labour's letter along with shadow Cabinet Office minister Rachel Reeves, also called on the committee to look into the decision to accredit Greensill to the CLBILS loan scheme.
The pair suggested the committee should look at "whether proper due diligence was undertaken on the firm's financial health by government".
They added that taxpayers "deserve to know the true extent of access to this current Conservative government that was afforded to Greensill Capital through the former prime minister".
Replying to their letter, Lord Evans said his committee "is an advisory body and does not have a remit to investigate individual cases".
But he added the committee would welcome suggestions from the party on improving transparency rules as part of an existing inquiry due to report in the autumn.
A government spokesman said Mr Greensill had previously acted as a supply-chain finance adviser and crown representative - adding the appointment had been unpaid and was approved in the normal manner.