Africa is covered in epithets, like graffiti. It has been labelled dark, lost, hopeless. But generalisations about Africa are dangerous. The only certainty is its size: it could contain the United States, China and India and still have room to spare. Recently it has been dubbed rising, hopeful, the continent of the future. But Africa cannot be declared successful until its vast, rich heart, the Congo, is peaceful and prosperous.

Most other African countries have more or less emerged from the uprisings and chaos of the 1990s that followed the end of the Cold War. But Congo lies broken and wasting. The last two elections have not produced a government capable of delivering services or security. The legacy of Mobutu Sese Seko's 32-year corrupt kleptocracy remains the zeitgeist of its ruling class. The people must fend for themselves.

Congo's potential, like most of Africa's, is immense and unmeasured. It has everything that the rest of the planet needs for the future; the highest reserves of mineral ore, thousands of square miles of fertile land and the second largest rainforest in the world. The energy of its huge, fast flowing river could power up much of southern Africa.

The knee-jerk reaction of Britain and other western countries is therefore to give Congo aid. And the only way of spending 0.7% of our GDP on aid is to give it to governments. But has Congo got a government? In 1997 the remnants of the Mobutu regime were pushed out by the armies of Rwanda and Uganda. They replaced him with Laurent Kabila, a former revolutionary and cafe owner, living in exile. When he rejected the Rwandans' tutelage, they had him murdered and replaced him with his son, Joseph.

To legitimise Joseph Kabila the aid donors paid for and organised two elections, each costing more than a billion dollars. In 2011 that came out of a national budget of £4.6 billion ($7.3 billion). The elections satisfied the western political need to give Kabila international legitimacy so he could now receive aid. But the elections in Congo divided rather than united. The losers saw them as fraudulent.

After the election supporters were rewarded, opponents shunned but they live in different parts of the country so a small war broke out. At the very moment when the country needed to come together, the western solution deepened the divisions. It also handed total political and economic power to a greedy elite incapable of constructing a viable state – even, as one Congolese academic said, in their own narrow interests.

What has wrecked the Congo is not lack of aid. It is politics. Aid has probably made things worse by offering development which may never be delivered. There is no state capable of delivering it. If ever there was a case for a country to be under a UN mandate, it is Congo. The United Nations' current half-baked, ill-thought-out mandate was cruelly exposed last week as UN troops stood back to allow rebels to take the city of Goma in eastern Congo.

But there was a second, even more catastrophic contradiction in western policy. After the Rwandan genocide, western governments, ridden with guilt, supported the incoming Rwandan regime, a rebel group led by the charismatic Paul Kagame. He now runs a capable state – perhaps too capable. Rwanda is a tightly controlled dictatorship, with almost no press or political freedom. But it uses aid well, it is not stolen. A succession of British aid ministers from Clare Short to Andrew Mitchell see Kagame as the saviour of Africa. They gave him money – currently £83m a year, knowing it will be spent on education, health and other good things.

Rwanda's success however is Congo's loss. Fearful that political opponents will gather in the forests and mountains across the border in eastern Congo, the Rwandan and Ugandan regimes have armed militias there, most recently the M23, Mouvement de 23 Mars. This militia protects the Tutsis of eastern Congo, Kagame's ethnic group, and guards mines and plantations controlled by senior Rwandan and Ugandan officers. They control and tax trade routes and bring the loot across the border to Uganda and Rwanda. Above all, they ensure that there is no order, security or justice in eastern Congo. Every village has a militia and many have turned into roving gangs killing, raping and stealing at will. Controlled anarchy in eastern Congo suits Rwanda and Uganda – as long as the anarchy does not get out of hand.

Unfortunately, and embarrassingly for the British and American governments, Rwanda and Uganda, their closest allies in the region, have been fingered by a well-researched United Nations report, as the suppliers of weapons to M23 as well as the beneficiaries of the free-for-all in eastern Congo. The US tried to suppress the report. The British suspended aid to Rwanda. On his last day at Dfid Mitchell restored it.

The war in eastern Congo is the worst war in the world, costing according to some estimates five million lives. It is time the US and UK took it seriously and played a more even and consistent hand in trying to bring peace.

Richard Dowden is the director of the Royal African Society and author of Africa; altered states, ordinary miracles

• This article was amended on 28 November 2012. The original said Mobutu Sese Seko was in power for 22 years. This has been changed to 32.