Measured speeches across the floor of the House of Commons yesterday reinforced cross-party recognition of the rightness and legality of the military intervention in Libya.

But repeatedly the still unanswered question was raised of how the endgame is to be achieved.

There is little doubt that the swift air attacks by France, Britain and the US following UN Resolution 1973 prevented wholesale slaughter of the rebels holding out in Benghazi.

There was consensus in the Commons, with MPs mindful that doing nothing was not an option and confident in the legal basis for the military action. No one needed a reminder of how crucially different this was compared with the invasion of Iraq. But continued cross-party support will be contingent on what happens next.

A no-fly zone has been established but history suggests such a policy is unlikely to secure regime change. The aim of the mission, to protect Libyan civilians, will remain unfulfilled as long as Muammar Gaddafi remains in power. Whether he can be a legitimate target has provoked a difference of military and political opinion.

General Sir David Richards, Chief of the Defence Staff, was clear this could not be the case while David Cameron suggested it could be legal "in certain circumstances". There is a legal and diplomatic tightrope to walk but the confused message indicates a potentially fateful lack of clarity underpinning the mission. The alliance was already starting to look perilously fragile following criticism by Amr Mousa, Secretary of the Arab League, about Saturday's missile attacks going further than intended. The danger of a rift among the allies was avoided by the offer of aircraft from Qatar yesterday but Mr Mousa's comments identified the elephant in the room at the Security Council and at the allied summit in Paris: how can limited military action to protect civilians achieve the desired end of removing Gaddafi?

The West, already committed in Afghanistan, has no stomach for prolonged military involvement in Libya and President Obama has reiterated that the US does not intend to lead the military action The lesson of Iraq is not just that military intervention must have a solid legal basis but that success requires a post-conflict strategy. France is right to insist the Arab league is kept onside.

Ultimately, as David Cameron insisted yesterday, the future of Libya must be determined by the Libyan people. Hoping that Gaddafi will go , however, does not amount to an exit strategy. There is a danger that the no-fly zone and the halting of Gaddafi's troops before they reached Benghazi could lead to partition in Libya. The situation will become not just politically unstable but with oil and water supplies controlled from Tripoli by Gaddafi and his sons, the people of Benghazi suffer an additional plight.

Revolution in Egypt and Tunisia was achieved without outside help and without tribal splits. The defection of three senior army commanders and several ambassadors to anti-government ranks in Yemen yesterday suggests the revolution there may be gaining strength.

For it to reach fruition in Libya will require clarity of purpose from the allies and a substantive involvement on the part of the Arab League.