The 44-year-old aid worker David Haines was seized in Syria in 2013 and was being held by ISIS militants who have already killed two US journalists.
The Foreign Office here in a statement said, All the signs are that the video is genuine.
The latest video showing his killing also includes a threat to kill a second British hostage, identified as Alan Henning. Cameron vowed to do everything possible to find the killers.
The emergence of the footage late Saturday night saw Cameron return to Downing Street after midnight.
He chaired a meeting of the governments emergency committee Cobra early Sunday and issued a statement afterwards saying the killing would not change Britains strategy against the ISIS.
It is an act of pure evil. My heart goes out to the family of David Haines who have shown extraordinary courage and fortitude throughout this ordeal, he said. We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes, he added.
They are not Muslims, they are monsters, Cameron said.
He described Haines, 44, as a British hero, and praised the extraordinary courage of his family.
Hainess family said he would be missed terribly.
David was most alive and enthusiastic in his humanitarian roles. His joy and anticipation for the work he went to do in Syria is for myself and family the most important element of this whole sad affair, his brother Mike Haines said in a statement released through the Foreign Office.
But while Cameron asserted that we have to confront this menace, he added that this will not involve direct British involvement in the US-led armed intervention in Iraq against the ISIS.
Britain is instead playing a supporting role to the US, providing transport and supplies.
US President Barack Obama also condemned the barbaric murder of Haines which in recent weeks has killed two American journalists James Foley and Steven Sotloff in the same manner.
Australian Prime Minister Tony Abbott said Hainess murder was further demonstration that this particular terrorist group does not just do evil, but exults in doing evil.
The French presidency said in statement that, The heinous murder of David Haines shows once again how the international community must mobilise immediately against the ISIS.
The ISIS, which seeks to establish an Islamic Caliphate across the Middle East, controls a large swathe of territory extending from the north and east of Syria, to almost all the mainly Sunni parts of Iraq.
The group controls a population of around 5 or 6 million people, including Iraqs second largest city, Mosul.
In north Iraq, Kurdish Peshmerga forces, helped by US air strikes, are slowly regaining ground they had initially lost to the ISIS.