Who was the first cabinet minister to resign from Tony Blair's government? No, it was not Peter Mandelson. He made a habit of resigning, but he was not the first to go. No, it was not David Blunkett either. No, for those of you who can't remember, I am not going to tease through the entire list of the many ministers compelled to quit during the Labour years. The answer is Ron Davies – remember him? – who resigned as secretary of state for Wales amid the most lurid headlines about his "moment of madness" on Clapham Common. That sudden departure from government was accompanied by a media storm of a similar intensity and duration to that which has just attended the downfall of Liam Fox. Then the waters closed over the head of Mr Davies and the Blair government sailed on without him to win two further elections.

Cabinet resignations seem to matter a huge amount at the time. They scream from the front pages, they dominate the bulletins, they even generate some good jokes. My favourite about the Fox affair is that he actually wrote his resignation letter a week ago, but made the mistake of giving it to Oliver Letwin to hand to the prime minister. Dr Fox finally went on Friday only because it took that long for someone to fish his letter out of the park bin into which the ditzy Mr Letwin had discarded it.

I'd say that the fall of Dr Fox had taken on an aura of inevitability from Tuesday as resourceful journalists began to join the dots between Adam Werritty, his best man and self-styled "adviser", and defence-related industries. I'd also say that Number 10 could grasp that too. Whatever Downing Street says to the contrary, David Cameron and his advisers have been obsessed with how to handle this affair. As for Dr Fox himself, the termination of his cabinet career will matter for the rest of his life. When he dreamed of his place in history, he did not have in mind that he would become the first defence secretary to be forced to resign because of scandal since Jack Profumo had to go in 1963 because of the lies he told about Christine Keeler. Technically speaking, Dr Fox is the first-ever defence secretary to be forced to resign because, in Profumo's day, the job had the more bellicose title of secretary of state for war.

In the grand scheme of things, most resignations from the cabinet don't have a discernibly lasting impact. They only do so if the voters and media draw from them larger conclusions about the government. The fall of Jack Profumo was one of those resignations which did have a greater meaning because it brought to a head and crystallised a wider feeling that Harold Macmillan's Tories had grown corrupted by being too long in office. It also led to the conclusion that a prime minister once famed for his assured political skills had lost his touch. Macmillan resigned a few months later.

Number 10 is very anxious that we should see no Profumo-like parallels. They want Liam Fox tagged, bagged and binned as a resignation which has no larger consequences and says nothing more deeply damaging about this government.

"It was a unique set of circumstances," says one adviser to the prime minister. Even as Mr Cameron was before the cameras expressing the ritual obsequies for a fallen colleague, other Tories were privately voluble that Dr Fox was "always a maverick", "a chancer", "committed the most dreadful errors of personal and political judgment" – in other words, the only conclusion we should draw from this affair is that Dr Fox was the author of his own demise. Since this also happens to be true, many may be inclined to agree that his case is unique.

Number 10 is quietly congratulating itself on the way in which the prime minister has handled the first resignation of a Conservative from his cabinet. Characteristically nervous about the right of his party, Mr Cameron did not want to get into the position of having to sack one of their champions. Dr Fox could have been a rallying point for discontent with the coalition if he had been sent to the backbenches looking like a victim or a martyr in the eyes of the right. So Mr Cameron commissioned an investigation by the cabinet secretary, probably not the retirement present that Sir Gus O'Donnell first had in mind.

This tactic has exposed the prime minister to two charges. One is that he was subcontracting his own responsibilities to police the conduct of his ministers to an unelected civil servant and this placed the cabinet secretary in the embarrassing and constitutionally dubious position of declaring whether a minister is fit for office.

The second charge is that Mr Cameron has revealed himself to be feeble and dithering when it comes to dealing with errant ministers because he did not act faster and fire Dr Fox when it was becoming daily more apparent that he had to go.

Prime ministerial weakness and indecision has been Labour's accusation, but made rather half-heartedly because Labour itself had not actually called for the defence secretary to resign. As it turned out, the media, which work to quicker deadlines and are often faster to the facts than inquiries by the cabinet office, accumulated evidence which was just too damning so Dr Fox went before Sir Gus had formally reported back to the prime minister. But the end result was still the one originally desired by David Cameron. He comes out of it looking like someone who waited for the evidence before he came to a verdict about a colleague, the defence secretary's blood is not on his hands and Dr Fox is sent to the backbenches looking like neither a victim nor a martyr, but a fool. Even Tories who share his Thatcherite views and initially rallied to him now accept that he did for himself.

The vacant chair at the Ministry of Defence has been filled by Philip Hammond, a solid, amiable, unflashy accountant who goes to drinks parties – the ones I see him at, anyway – accompanied not by his best man, but by his wife. From a Number 10 point of view, that is a damage-limitation job well done. Wound cauterised. Case closed. Please move along. Nothing more to see here. They hope we will forget Liam Fox's resignation as quickly as we did that of Ron Davies.

I wonder about that. For there are some wider lessons to be learned and David Cameron would be sensible to absorb and act upon them before another scandal of a similar nature comes along. To start with, this affair has exposed a glaring omission in the ministerial code of conduct: it covers conflicts of interest that may arise from the activities and interests of spouses and other family members, but not "friends". This did not seem to matter in the past, but surely does in a government in which some ministers appear to be closer to their friends than they are to their spouses. The prime minister surely ought to ask the cabinet secretary to have the code rewritten to close that loophole. And get it done by Monday evening.

It is also high time, as is argued in the leader comment opposite, that David Cameron made good on his previous pledges to introduce robust laws to control the activities of lobbyists and clean up what he once called "crony capitalism".

I don't say all Tory ministers display such a cavalier disregard for the rules as Dr Fox. At least I bloody well hope they don't. But he was not quite so entirely untypical as it would suit the prime minister to have us believe. Dr Fox has not been the only cabinet minister to give the impression that he believes that only "the little people" have to obey the rules.

Most voters will not have followed every twist and turn of the Fox hunt, but some of the details are liable to resonate in the public consciousness. Secret meetings with controversial American tycoons at gold-plated hotels in Dubai. Trips on private jets paid for by more rich men, often based abroad. Undeclared encounters with foreign potentates at more five-star hotels.

This is not the lifestyle of most voters. These are the sort of things that tend to stick in the public mind because they confirm suspicions that people already harboured about Tories.

I don't say that every Conservative minister has the same appetite for luxury globetrotting or unusual friendships as Dr Fox. But he is not the only senior Tory who has hitched rides on rich men's jets. Some of the plutocrats who financed his best friend's activities turn out also to be funders of the Tory party.

The downfall of Liam Fox prompts us to remember that George Osborne almost did for himself with a dangerous liaison on a Russian oligarch's yacht and that David Cameron himself has had to apologise for getting too snug with media moguls.

So I don't think we are all going to be entirely persuaded to see this in the way Number 10 would like us to see this, as no more than the case of one exceptionally foolish cabinet minister who went rogue. There are patterns here. This resignation brings them into sharper relief. And we will all be looking that much harder in future for who next in the cabinet might repeat them.