Nato's mission in Libya looks like a foreign policy success for David Cameron, but that is not the same thing as having a successful foreign policy.

First, the obvious caveats: it is early days; the battle is not over, let alone the war. There are easily enough military and diplomatic traps ahead for the Libyan intervention to become a failure. The prime minister, the deputy prime minister, the foreign secretary and the defence secretary have all said as much. But for now, the politics of the situation are favouring Cameron. He took a big decision under considerable pressure and, after some nerve-wracking months, it appears to have paid off. "He definitely leapt before he looked," was how one senior Ministry of Defence official put it too me early on in the campaign. (The same source also said of the anti-Gaddafi rebels "the only good fighters among them are the al-Qaeda ones", a slightly wild allegation which should nonetheless be reason enough to put blind optimism for the future on hold.)

Libyans will decide whether they are better off in the long run for the UK's military partisanship in their insurrection-cum-civil war. The point is that, in the eyes of the British public, Cameron has effectively led a short war. There are usually political dividends to be drawn from that position.

But I suspect they will be limited in this case because, as with so much of Cameron's leadership, the good news story doesn't slot into a wider strategic narrative. It is worth remembering that the Conservatives came into power signalling reluctance to reshape the world - a la Blair - by military excursion. The new doctrine, as spelled out by William Hague in a series of speeches in July 2010, was a kind of bilateral mercantilism. The UK would continue to promote freedom and democracy around the globe, the foreign secretary said, but the main tool would be aggressive pursuit of trade interests. Overseas embassies would be reconfigured as pushy chambers of commerce.

Barely weeks before taking action in Libya, Cameron declared: "I am not a naive neocon who thinks you can drop democracy out of an aeroplane at 40,000ft." The fact that Cameron then decided to use British military assets against Gaddafi doesn't signal some visionary conversion to fanatical interventionism. Libya might be a one-off; Gaddafi might just have been low-hanging despotic fruit.

To get the maximum political advantage from the intervention, Cameron has to frame the episode in terms of his vision of Britain's role in the world - and it isn't clear that he has one. The project of expanding our national influence by trade is looking trickier as the global economy falters. As an ambition it is of a pair with George Osborne's hope of rebalancing the economy and driving growth through exports - which relies on a level of overseas demand for UK goods that has not yet materialised.

A big gap in Cameron's world view (at least the publicly known portion of it) is his sense of how Britain's position in the European Union will evolve as the single currency lurches ever onward in financial and institutional crisis. As I mentioned in my column this week, this omission is stirring dissent in the party. A lot of Tories see the eurozone crisis as an opportunity to start a wholesale renegotiation of Britain's EU deal, but there isn't much appetite for that at the top of the party. (This is partly because the leadership's view of all matters EU is coloured by their "modernising" crusade in opposition, so there is an association between public expressions of fierce euroscepticism and unelectability. Then, of course, there is the problem of the stubbornly Europhile Lib Dems.)

The Arab Spring; global economic turbulence; structural crisis at the heart of the European Union - three giant themes that raise profound questions about Britain's position in the world. What kind of a power do we want to be? How do we achieve that ambition? I don't get the impression that Cameron is any closer to having persuasive answers to those questions than he was when he moved into Downing Street last year.