What are British forces doing in Libya now?

David Cameron looked comfortable and at ease in the House of Commons chamber on Monday afternoon when updating MPs on what has happened in Libya over the summer.

And well he might: the rebels have overtaken Tripoli, Gaddafi is on the run, and the one major controversy – the discovery of papers suggesting British intelligence colluded with the Gaddafi regime in the rendition of terror suspects – happened under the last government.

But as soon as one set of questions about the conflict ends (even Richard Ottaway, the chair of the foreign affairs select committee, who has always been sceptical of the conflict, gave the prime minister credit for the way it has turned out), another begins: namely what happens to our troops now?

Cameron was keen to stress that the fall of Tripoli did not mark the end of the conflict and that British forces would continue to bomb targets to ensure the safety and security of the Libyan people.

The job is not over… pro-Gaddafi forces still pose a threat and in particular control the towns of Bani Walid, Sirte, and Sebha in the south. The NTC has been working to negotiate a peaceful outcome. But their leaders have explicitly requested that Nato continues its operations to protect civilians until that is achieved.

Over the weekend RAF Tornados struck eight military command and control installations South-West of Waddan and nine weapons and ammunition stores near Sirte.

But the threat being posed by pro-Gaddafi forces is unclear. Nato countries appear to have little evidence that civilian populations in the cities still under their control are being targeted.

Rather, officials warn of the “potential threat” posed as long as the pro-Gaddafi forces are armed. A Number 10 spokesman on Monday insisted British forces were not focused on finding Gaddafi himself, but refused to rule out the idea that some UK military assets could be used in the hunt for the former dictator.

How long could this situation go on for? If Gaddafi manages to evade capture, how will we decide whether those that retain some loyalty to him pose a threat to civilians? And even if he is captured, could we end up stuck in a civil war trying to ensure that his loyalists don’t launch a damaging counter-attack?

As Cameron bathed in the congratulation in the House of Commons on Monday afternoon, he made sure to avoid saying two important words: mission accomplished.