Labour has accused the government of being too complacent about the lobbying crisis after a cabinet minister claimed the current rules were “pretty good” and “quite robust”. George Eustice, the environment secretary, used the phrases in interviews in which he also defended David Cameron’s lobbying on behalf of Greensill Capital and played down the need for any wide-ranging reform of the Whitehall probity rules. The inquiry ordered by No 10, which will be chaired by the corporate lawyer Nigel Boardman, is one of seven now being carried out by the government, parliamentary committees and independent watchdogs into issues raised following the revelation that the former prime minister lobbied the chancellor via text message on behalf of Greensill, his employer. Boris Johnson has been warned that the “sleaze” revelations, which have also shown that some civil servants have been allowed to take on lucrative private sector work while also employed by the government, could be an electoral liability. Eustice, who has not been personally implicated in any of the lobbying stories, sought to play down their significance in interviews on Sunday morning with Sky’s Sophy Ridge and the BBC’s Andrew Marr. He told Ridge: “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.” There could be “tweaks or changes” to the current rules, he conceded. But he said the Boardman review “doesn’t need enforcement powers”, and he did not even expect it to make policy recommendations – although some of the other inquiries being launched would, he suggested. No 10 later corrected Eustice, saying the Boardman inquiry terms of reference did allow it to make recommendations. Eustice told Marr that, as a result of changes made when Cameron was prime minister, there were already “some quite robust systems in place”. When Cameron was PM the Lobbying Act was passed creating a compulsory register for people working as lobbyists. But that rule only covered third-party lobbying, not the much more common in-house lobbying of the kind Cameron was engaged with on behalf of Greensill. Rachel Reeves, the shadow Cabinet Office minister, said Eustice’s comments in his interviews amounted to his shrugging his shoulders and saying: “Scandal? What scandal?” She went on: “The public know that the cosy 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 honour back into heart of government.” The Eustice interviews coincided with the Sunday Times publishing an email that Cameron sent in April last year to Matthew Gould, the head of NHSX, the health service’s digital services arm, asking if Gould could help enable a Greensill app, Earnd, get access to NHS payroll data. Cameron, who has stressed that he promoted Greensill services because he thought they were of value to the public and government, said Earnd would provide “a material benefit across the NHS” because it would enable staff to access their pay early. But, despite the email, NHSX did not sign up centrally to the Earnd scheme, and Greensill has now gone into administration. In his interview with Marr, asked if he thought Cameron had done anything wrong, Eustice, who was press secretary to Cameron when he was opposition leader, said: “The key thing is he’s not broken any of the rules.” He said that Cameron left office five years ago and that he was entitled to find another career. When it was put to him that as a former prime minister Cameron would have much more clout when lobbying Whitehall than other people, Eustice replied: “I think what most former prime ministers find is the tide goes out on their power quite quickly.” At the weekend the Cabinet Office also confirmed that Francis Maude, the former Conservative minister, is no longer advising the government on Whitehall reform. The announcement came after Labour queried the potential conflict of interest, because Maude also runs a consultancy, but government sources claimed that Maude’s unpaid role advising the government ended last autumn when his proposals were fed into the review process.