Prime Minister David Cameron on Sunday called the murder of a British hostage by Islamic State militants an "act of pure evil" and vowed Britain would do all in its power to bring the killers to justice.

"This is a despicable and appalling murder of an innocent aid worker. It is an act of pure evil," he said in a statement released by his Downing Street office.

"We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes."