The response of Prime Minister David Cameron yesterday to the murder of the hostage David Haines was swift and clear:

Mr Haines's killers are not Muslims, he said, they are monsters; the terrorists behind the murder have planned and continue to plan attacks across Europe and in the UK; and the British government cannot ignore the threat to our security. "We will hunt down those responsible," said Mr Cameron, "and bring them to justice no matter how long it takes."

He is certainly right to say Britain cannot ignore the threat. Some 500 British people are estimated to have travelled to Iraq and Syria, including the 20-year-old Glaswegian Aqsa Mahmood; the terrorist who appeared on the video with Mr Haines may also be British, and Mr Haines, who lived in Croatia but had strong links to Scotland, was just one of the many Britons who work with humanitarian organisations in the region. His murder, and the wider issues that led to it, are connected to us all.

The question now is what can be done to prevent another hostage dying in the same way as Mr Haines, and Mr Cameron yesterday laid out several strategies. On air strikes, he appeared to be no closer to authorising direct British involvement; instead he indicated British aircraft would continue to help with intelligence gathering and logistics. In due course, there may be a case for reviewing that policy, although we know that, whether the UK is involved directly or not, air strikes alone will not deal with the problem of a murderous, radicalised man on the ground with a knife in his hand.

Mr Cameron also said the UK would continue to work with the Iraqi government to ensure it represents all its people, which must surely be an acknowledgement of Iraqi PM Nouri al Maliki's failure to do so. The crisis in the region is partly due to Mr Maliki's discrimination towards minorities, with Islamic State (IS) winning support from disgruntled Sunnis. Anything the British government can do to prevent the incoming Iraqi government from repeating this mistake will be welcome.

Another stated strategy of the British government, Mr Cameron said, is to work to mobilise international support to bear down on IS. He did not say so explicitly, but this must increasingly mean considering the option of dialogue with the regimes of Iran and Syria. Russia will also have a role to play because of its influence with President Assad of Syria.

Finally, Mr Cameron said the most important of his government's strategies was to maintain and continue to reinforce the counter-terrorist effort at home to prevent attacks and hunt down those who are planning them.

Some of this will involve surveillance work to prevent radicalised Britons returning home and posing a threat, but surveillance work alone is not the complete answer: appeals from Muslims to Muslims to turn away from extremism are also important. As Mr Cameron says, the government must work with its allies in the Middle East, but it must work with its allies in the UK too.