In May 2008, just a week after being elected mayor, Boris Johnson received a an invitation from City lobbyist Roland Rudd: "Would you like to have dinner with me and a small group of senior chairmen and chief executives who would be fascinated to hear your plans for London," wrote Rudd.

Johnson was "pleased to accept" and duly cycled to Rudd's grand house in Kensington for a 7.30pm "meet and greet". After 25 minutes, the guests were seated, and at precisely 8.05pm, starters served. Ten minutes passed before Rudd made introductions, and at 8.20pm Johnson said a few words ("standing at the table"). At 8.25pm, the mains arrived. Boris was away by bike at 10.30pm. This much we know (from documents released by the mayor's office under freedom of information). What we don't know is what was discussed in the course of the three-hour dinner: what information was shared, and on which policy matters the mayor was lobbied. Were any promises made or deals struck?

And now we are to know the supper arrangements of the prime minister, who has offered to publish quarterly his dinners with donors. Don't be fooled. We will similarly learn very little of consequence from such disclosure. More importantly, this small offering of transparency is being served up by the government at a time when it is actively engaged in limiting public scrutiny of lobbying.

What's demanded by this latest scandal is disclosure of discussions between politicians and private interests over government policy. And not just over dinner with the PM, but anywhere and anytime and with anyone in a position of power – the chancellor, other ministers and civil servants.

No amount of tweaking of the rules for politicians and officials will give us what's needed – a comprehensive picture of who is influencing which policies. A little bit of crisis-induced transparency here and there is not going to cut it. One sensible solution, which has actually made it to the table, is to require disclosure from those doing the lobbying. In short, a register of lobbyists.

But the government's plans to regulate the influence industry with a compulsory register of lobbyists, published last month, are a sham. As proposed, they would cover only a quarter of lobbyists – only those working for third-party clients in agencies; and would require no meaningful information to be revealed – only who is lobbying, not whom in government they are targeting or what they are lobbying for. They have been widely condemned. A register should require anyone seeking to influence government to reveal who is lobbying whom, over what and how much they are spending doing it (with sensible, obvious exemptions). It's pretty straightforward; other countries have operated lobbying registers for years. We desperately need one here.

It's perfectly legitimate for Tory donors, or anyone else, to make their case to politicians for changes to government policy, whether its over employment rights, cuts to corporation tax or planning reforms. But not if it's done in secret. A robust statutory register would require them to make their lobbying public.

Private interests make a tactical investment in lobbying – whether it is payments to parties, behind-the-scenes contact-building or well-funded public campaigns – to influence government decisions that benefit their bottom line. They are currently seeing a generous return on their investment. For Cameron to offer up his diary as a solution to this is an insult to the public.

• Follow Comment is free on Twitter @commentisfree