It is easy to be pessimistic about Somalia. It is the exemplar of a failed state. It has existed in anarchy since opposing clans overthrew its government in 1991 and failed to agree on what should replace it. It is bedevilled by chronic food shortages thanks to the Horn of Africa's worst drought for six decades, with millions on the edge of starvation.

Hundreds of thousands have fled to squalid refugee camps in neighbouring countries. Pirates patrol its lawless coastal waters, costing the international economy billions in ransoms. Rent-seeking warlords fight over its territories. Large tracts of land and their inhabitants are under the sway of the Islamist fundamentalist fighters from the al-Shabaab group. Small wonder it has been called the "world's worst failed state".

For all that, there has been some progress. Troops from the African Union have taken over al-Shabaab's strategic stronghold and are forcing its fighters out of populated areas and back into the desert wastes of the south-west. Navies from around the world have sent warships to patrol the Somali coast, while international shipping lines now have armed guards aboard their vessels. Even so, a formidable task faced the world leaders' summit on Somalia in London yesterday. It was not fully discharged.

The conference was prompted by concerns over the threat to British interests in the region and to wider global security. Pirates are only one part of the problem. Al-Shabaab has recently proclaimed affiliation to al-Qa'ida. And MI5 is concerned about a Somali-linked bombing campaign in London during the Olympic Games in July. David Cameron spoke yesterday of "young minds... being poisoned by radicalism, breeding terrorism that is threatening not just Somalia but the whole world".

The Prime Minister is right to be worried. There are more British passport-holders engaged in terrorist training in Somalia than in any other country. But it is not only Britain that is under threat. There are also large émigré populations of Somalis causing concern in neighbours such as Kenya and Ethiopia.

Conditions in Somalia are dire indeed. It is one of the world's most deprived states; half the population struggles to survive on less than a dollar a day and almost one in three depends on emergency food aid; its health statistics are among the worst in the world. Britain's efforts are laudable enough, with the focus on plans to launch air strikes on al-Shabaab camps, and on efforts to replace the existing transitional government with a "caretaker authority" to draft a constitution, hold a referendum on it, and run the subsequent elections. But they are insufficient to meet the challenges of a country torn apart by famine and civil war.

Even less encouraging is the fact that this is not the first international summit on Somalia. All its predecessors have produced is a succession of weak transitional governments lacking in popular legitimacy and wholly unable to rescue the country from lawlessness and clan warfare.

This time, at least, there are several Muslim states involved. But yesterday's meeting still had no suggestions except military containment for combating al-Shabaab. It did not address the politics of who is arming the Islamists and how. Neither did it identify the emerging leaders who must manage any political transition. Nor has it demonstrated any proper awareness of the need to work with the quasi-autonomous areas of Somaliland and Puntland. It has not even offered any serious initiatives on how to help local populations see the economic benefit when al-Shabaab is pushed out.

Sadly, agreements on piracy, security and aid are not enough. And this London conference will go down as a missed opportunity.