The Financial Times and Sunday Times newspapers have reported that former leader David Cameron contacted ministers on behalf of finance firm Greensill Capital, including sending text messages to finance minister Rishi Sunak and arranging a drink between banker Lex Greensill and Health Secretary Matt Hancock.
Cameron, however, has denied breaking any code of conduct or government rules.
British Prime Minister Boris Johnson has been warned the revelations, which also show some civil servants have been allowed to take on lucrative private sector work while they were employed by the government, could be an electoral liability.
The behavior of Cameron and other officials have raised questions over whether former ministers and civil servants are granted easy access to the Conservative government.
In an interview on Sunday morning with Sky’s Sophy Ridge, George Eustice, the environment secretary, sought to play down the significance of the matter.
"The real point is has he (Cameron) really done anything wrong? Well on the face of it no, but there's a review going on, we mustn't prejudge that," Eustice told Ridge.
"But fundamentally I think that the systems we have place with ministers declaring interest, with the ministerial code and the focus on that and how ministers conduct themselves in office, is actually a pretty good one.”
He went on to say that there could be “tweaks or changes” to the current rules.
“The public know that the cozy relationship between the Conservative government, commercial lobbyists and taxpayer money stinks of sleaze. It’s one rule for them, another for everybody else."
“We don’t need the ‘tweaks’ Eustice said they might consider today, we need to tackle Tory sleaze with a full, independent, transparent inquiry – and we need stronger measures to put integrity and honor back into heart of government,” Reeves added.
Johnson has launched an independent review to look at the accusations and several parliamentary committees are also launching inquiries into the role of lobbyists and ministers' interests in private companies.