The footage released online shows the man waving a gun as he references Britain’s “handful of planes” carrying out air attacks on IS targets in Iraq and Syria.
The footage, which has yet to be independently verified, then shows five men “confessing” to filming and photographing sites in exchange for money within Raqqa, the capital of the Islamic State group’s self-declared caliphate.
Dressed in orange jumpsuits, they are then made to kneel in the desert before being shot in the head by masked men.
Addressing the prime minister, the “British” jihadi says: “How strange it is that a leader of a small island threatens us with a handful of planes. One would have thought you would have learned the lessons of your pathetic master in Washington and his failed campaign against the Islamic State.
“But it seems you, just like your predecessors Blair and Brown, are just as arrogant and foolish. In fact David, you [waves handgun] are more of an imbecile. Only an imbecile would dare to wage war against a land where the law of Allah reigns supreme and where the people live under the justice and security of the sharia.
“Only an imbecile would dare to anger a people who love death the way you love your life.”
The masked man is the latest purported IS figure appearing to have British roots.
“Jihadi John”, the British extremist Mohammed Emwazi, appeared in videos showing the execution of Britons David Haines and Alan Henning, plus those of US journalists James Foley and Steven Sotloff. Emwazi was killed in a US drone strike in Syria in November.
It has been suggested the video was an attempt to distract attention from recent military setbacks IS has faced, like losing control of the Iraqi town of Ramadi.
In the latest video the man goes on to say that IS will invade the UK and rule under Sharia Law.
He adds: “As for those of you who wish to continue fighting under the banner of Cameron, on the minimum wage, we say to you, to ask yourself, do you really think your government will care about you when you come into our hands? Or will they abandon you, as they have abandoned these five and those who came before them? Because you will lose this war, as you lost in Iraq and Afghanistan.”
It comes days after Cameron promised to crack down on IS sympathisers, stressing in a New Year’s message that all Britons should have “loyalty” to their country.