Gordon Brown and South Africa's Thabo Mbeki spent a couple of hours in conversation the other day, talking, it is reported, about the crisis in Zimbabwe. It is the mark of an authentic statesman to be able to speak fluently for two hours without saying anything remotely useful.

In Zimbabwe itself, meanwhile, the cops have been chatting with seven election officials. According to the police, who allege fraud and "criminal abuse of duty", the functionaries have some explaining to do. How could they preside over a presidential election in which Robert Mugabe was a participant and fail to come up with a result appropriate to his vast popularity?

Voting outcomes have yet to be certified or published, but the cops are confident that some 5000 papers were miscounted by the mendacious officials. When you have Zanu-PF's extensive experience in stuffing ballot boxes, you tend to know about these things.

The arrests are part of an emerging pattern. Far from cutting a deal that would allow the "Marxist" octogenarian to be reunited with his "holiday home" in Malaysia, Mugabe - encouraged, no doubt, by his 40-strong client politburo - means to fight on. He could escape justice: so much is conceded. But those who populate his army and his security apparatus would not be so lucky. There are many deaths, starting with the massacre of 25,000 souls in Matabeleland in the early 1980s, still to be explained.

So election officials are charged with the crime of failing to arrive at the right result. So the remaining white-owned farms come under attack. So the suspiciously young "veterans" of the liberation war, complete with an energetic "green bombers" youth cadre, are mobilised while police and army threaten to ignore any election results not to their liking.

Morgan Tsvangirai, candidate for the Movement for Democratic Change (MDC), says a war is being prepared. Having been beaten senseless once before by Mugabe's patriots, Mr Tsvangirai has experience on his side. Efforts to rig the elections having failed - the camera-phone is a useful gadget - it seems the great liberator has decided to forget about plausibility, credibility, legitimacy or pride.

It is unfair, of course, to say that Mr Brown has failed to "act". What could Britain do? Mugabe has adopted what might be termed the North Korea strategy: there is nothing the international community can now inflict on his country and his regime that would approach the damage the latter has already wrought on the former.

Military intervention, even by Zimbabwe's neighbours, is probably out of the question. Diplomacy has been comical, shameful and futile by turns. Economic action would be a joke - with a single important exception - in the context of a country that has added a new chapter to the annals of hyper-inflation.

Still Mugabe insists on blaming the former colonial power for all his country's ills. There was some truth to the rhetoric, once upon a time. White ownership of vast tracts of Zimbabwe did not come about by accident, or by anything resembling legal process. By any reasonable definition, much of the land was stolen. It needs to be, in the proper sense, repatriated.

But Mugabe has instead replaced one form of corruption with another, arguably worse, version, awarding white farms to his incompetent favourites while driving Zimbabwe to ruin. That cannot be explained, even if you choose to believe the excuse, by foreign conspiracies. Britain and the other colonial powers can be held responsible for many things, but not self-inflicted bankruptcy and endemic poverty in a rich and fertile land.

Zimbabwe is an African problem. It is patronising to Africans, and self-defeating, to say otherwise. This is not another story about the abuse of aid and trade. This is not the work, for the most part, of the trans-nationals, the Chinese or interfering white governments. Mugabe was never Britain's favoured successor to racist rule, but he came to power on a wave of popularity and acclaim. Some of us even thought him a hero, and considered that a Bob Marley song was the least Zimbabwe's rebirth deserved in 1980. All that seems fantastic now.

Britain claims to be assembling one of those "£1 billion" (nice round number) aid packages in preparation for the moment Mugabe yields to reality. If the act matches the press release, if double-counting, pre-conditions and the usual vices attendant on western benevolence are absent, that sounds reasonable. One of these days Mr Tsvangirai will need all the help he can get. For now, however, Zimbabwe's crisis is embodied in one figure, and its solution in the hands of another.

Thabo Mbeki appears not to realise that he bears responsibility for his own revolutionary legacy. Aids denial in the South African context was bad enough. ANC corruption and assaults on press freedom have been, to put it no higher, deeply dispiriting. But the insistence that Mugabe should be taken at his own estimation, that he should be indulged year after year in the face of all the evidence, that he should earn applause when African leaders meet, disgraces Nelson Mandela's movement.

Only South Africa can halt Mugabe. It controls the only important border, holds the last economic reins and provides the Zimbabwean regime with its only important source of legitimacy. Mr Mbeki need say only that he is unimpressed by Mugabe's response to the election process, that he deplores alleged assaults on 80 opposition activists, that the courts should not be required to validate a democratic poll. Nothing of the sort has happened.

For years, Mr Mbeki has been making vaguely hopeful noises over "progress" with Mugabe. The strategy, if any, seems to rest on the hope that an old man will recognise his mortality, or simply die. You can judge how effective this has been by the simple fact that Mugabe is neither intimidated nor dissuaded by South Africa's words and deeds. An absurd delay in announcing election results? Mr Mbeki says this is to ensure there is "no controversy". A re-run allowing time for Mugabe to rig results? Mandela's heir says it is "time to wait".

We can presume that Mr Brown and the South African president failed to agree on that. It is less likely that the Prime Minister made a broader point: Africans dealing with African problems have not, in this case, done much to comfort an African people. They have failed, are failing, and seem content to live with that failure even while Mugabe mocks their rhetoric. In the process, they confirm all the latent (and not so latent) post-colonial racism of the west. If nothing else, they excuse our impotence.

It amounts to a very sad story. The last thing Africa needs is another failed state. You could talk, as Tony Blair once did, of a "scar on the conscience of the west". There comes a point, however, when you need to talk about the conscience of Africa itself, and the conscience of its biggest regional power. If nothing else, simple pragmatism applies: does South Africa need a desolated country on its doorstep simply because Mugabe was once a hero who called the white world's bluff?

It appears that Mr Mbeki can live with that. It is clear, beyond mere appearance, that the people of Zimbabwe cannot.