It follows allegations that an MP and three members of the House of Lords agreed to do parliamentary work for payment.
Deputy Prime Minister Nick Clegg has said he and the Prime Minister were ‘determined’ it should go ahead.
“The public have a right to expect transparency and a basic level of dignity from our politicians, officials, and other public servants,” said Mr Leigh.
“A clear set of rules should be agreed upon and vigorously enforced, otherwise the political class risks alienating even further the people we are chosen to represent.”
“I look forward to considering any new proposals that will come forth and I think they deserve a fair hearing,” he added