Boris Johnson’s former anti-corruption tsar, who resigned last week, has called for urgent reform of the standards rules around lobbying, as well as more scope for the independent adviser to hold the prime minister to account.

John Penrose, a Conservative MP and former minister, said it was extremely important for democracy to fix problems with the UK’s standards regime affecting ministers, MPs, advisers and civil servants.

In particular, he called for tougher anti-lobbying rules, as recommended in a report by Nigel Boardman over the Greensill scandal and the Committee on Standards in Public Life (CSPL).

Johnson’s anti-corruption champion since 2017, Penrose stood down from his role last Monday after objecting to Johnson’s perceived failure to address the Sue Gray report’s finding that he showed a lack of leadership over lockdown-breaking parties in No 10 and concluding that this appeared to be a breach of the code.

Johnson’s independent adviser on ministerial interests, Lord Geidt, had said he felt unable to offer his opinion on whether Johnson had broken the code, because he might have felt compelled to resign if his advice were not followed. This would have placed the code in a position of “ridicule”, he claimed.

Speaking afterwards, Penrose said he thought the government’s most recent changes to the adviser’s role, allowing him to recommend initiating an investigation were “a lot stronger than before and I think in practical, pragmatic British terms, we should give it a chance to work”.

However, he said there were “new problems which have only just appeared in the last couple of days” around the adviser feeling unable to pass judgment on whether the prime minister has broken the rules.

Penrose suggested that the adviser should not have to resign if his advice were not followed, in the same way that Sir Chris Whitty, England’s chief medical officer, was not expected to stand down if politicians took a different view to him.

But he said: “The adviser should be expected to advise on whether any prime minister has broken the ministerial code or not, just like they do for any other government minister already. At the moment the prime minister has an exception, and that means there’s no public advice for parliament and everyone else to see, which isn’t fair at all.”

On wider changes to the standards regime around lobbying, Penrose said ministers should have to sign legally binding declarations that they would not lobby the government for fixed periods after leaving office – making mandatory the advice given out by the Advisory Committee on Business Appointments (Acoba).

“Acoba isn’t fully legally binding at the moment, and it ought to be. So what Boardman has suggested is that civil service contracts should make Acoba’s decisions binding and, because ministers aren’t technically employees, the equivalent for them is that they sign a legal deed that says: ‘I will be bound by the decisions of Acoba.’ It’s a nice, simple way of giving Acoba the teeth and claws it needs,” he said.

Secondly, Penrose called for a more detailed, transparent and easily searchable record to be published of meetings between companies or lobbyists and members of the government. He said not just ministers but political advisers and senior civil servants should be subject to such scrutiny.

“These are low-cost and easy steps that don’t need new legislation, and would be a huge boost to transparency and confidence in our institutions,” he said.

Urging the government to respond to the Boardman report, which was published in the middle of last year, as well as addressing more of the CSPL’s recommendations, Penrose added: “Fixing these problems is probably more important now than it has been for years, not just for our current government, but for our entire democracy too.

“Ministers have promised to respond to these reports, so let’s just get on with it. It’s an opportunity to do the right thing, and ‘do well by doing good’, and it won’t cost the taxpayer a bean either.”

Parliament has been hit by numerous lobbying scandals in recent years including the Greensill scandal, which involved the former prime minister David Cameron lobbying former colleagues by text message on behalf of his employer, a finance firm which has since collapsed.

The government was also drawn into a controversy over Owen Paterson, a Tory former cabinet minister, who was found to have lobbied government ministers on behalf of two companies. No 10 tried to orchestrate against Paterson being suspended from the Commons, which backfired and led to Paterson’s resignation and the loss of his safe seat in a byelection.