Leading article: Mr Cameron's Libya mission remains far from accomplished

So far, the Prime Minister has had a good war in Libya.

It was apparent from the start that both he and his co-warrior, the French President, Nicolas Sarkozy, were concerned to avoid the pitfalls that doomed the early stages of the US-led invasion of Iraq – Mr Sarkozy as a member of the French government that opposed the Iraq war; David Cameron all too aware of the political damage it had inflicted on Tony Blair. That they managed to secure the defeat of Gaddafi without deploying ground troops – except special forces – without causing large numbers of civilian casualties, and without stealing the glory from the Libyan fighters, is about as satisfactory an outcome as they could have hoped for.

No wonder, then, that both Mr Cameron and Mr Sarkozy appeared confident and comfortable as they presented the relatively meagre results of their "Friends of Libya" conference in Paris on Thursday. With Tripoli now under opposition control, only the Gaddafi heartland around Sirte holding out, and a transitional authority – the Transitional National Council – more or less in place, Libya is clearly not going back to its recent past. Interviewed on the BBC Today programme yesterday, the Prime Minister supplemented that shared sense of ease with a distinct air of vindication.

In one respect, Mr Cameron is entitled to feel justified. He and his ministers came under a rhetorical bombardment, in private and in public, from unhappy service chiefs who warned of overstretched resources that would make Libya mission impossible. Whatever the cost of the operation to the Exchequer, the Government's hand on the feasibility of military spending cuts is now strengthened. As he spelt it out yesterday, Britain played its part without the aircraft carrier that he had kept being told by service chiefs was essential. It had been his judgement against that of influential figures in the top brass. He will be emboldened to stick to his guns in the event of new battles against high-spending commanders in future – which is no bad thing for any government.

In almost every other respect, however, it is hard to resist the temptation to warn: steady on. These are very early days. The war for Libya's future is not yet won. In many ways, it is only now beginning. While it has gained wide international recognition, including from Russia, the TNC has not yet even moved completely to Tripoli from Benghazi, let alone started to govern. Celebrations for the end of Ramadan were accompanied by the first signs of potential unrest over the lack of basic services and the shortage of cash. For the moment, there is no sign of anyone relinquishing their guns.

Ensuring reliable supplies of electricity and clean water has to be one priority and the partial unfreezing of Libya's assets abroad is a positive move. But the TNC has yet to show that it commands the authority it will need to administer the country. Its pledges of tolerance, reconciliation and elections within eight months must be honoured. Meanwhile the "friends of Libya", including Britain, France and the United States, have not only to say, but to show, that they can take a back seat, albeit one that is supportive. With hints of an unseemly scuffle for privileged access to Libya's natural resources already apparent, that will be far easier said than done.