The head of a watchdog which monitors the activities of people in public office says the rules for ministers need to be tightened.
Lord Evans, chair of the Committee on Standards in Public Life, said it is “difficult to legislate for morality” following recent reports of lobbying by former prime minister David Cameron, and links between health secretary Matt Hancock and a firm which won NHS contracts.
Speaking with BBC Radio 4's Westminster Hour, Lord Evans said present oversight standards required improvements, including the fact the Prime Minister's independent adviser on ministerial interests - a post that has been vacant since November - does not have the power to start investigations.
"At the moment they have to wait to be asked and that means the perception might be this is not as independent a role as it might be," Lord Evans said.
"I think there's an opportunity there to modernise this role and to ensure that they are able to allay public concerns as they arise."
Former Cabinet Secretary Lord Wilson joined calls for a tightening up on lobbying and agreed the independent adviser "should be given the power to initiate investigations".
In a letter to The Times, Lord Wilson, who was Cabinet Secretary from 1998-2002, said while lobbying was "an inevitable part of public life" there had to be "no hint of corruption, no suggestion of cosy deals without due process, no suspicion of 'old boy' networks".
"Although it is difficult to legislate for morality, the Greensill and other affairs now emerging certainly suggest a need to toughen our safeguards. Greater openness is important," Lord Wilson wrote.
He added he would "ban any former minister or senior official from lobbying government on behalf of any business that was paying them in whatever capacity".
Links between ministers, officials and businesses are under intense scrutiny following the collapse of Greensill in March and revelations about former prime minister David Cameron's lobbying activities for the firm.
Labour has also levelled accusations of "cronyism" within the Government, raising concerns about procurement during the pandemic while also calling for a full inquiry into the Greensill saga.
The post of the Prime Minister's independent adviser on ministerial interests has been empty since November when Sir Alex Allan resigned after Boris Johnson stood by Priti Patel in a bullying row surrounding the Home Secretary.
A report authored by Sir Alex had found her conduct "amounted to behaviour that can be described as bullying".