The Church of England has delivered a withering critique of David Cameron's Middle East policy, describing the government's approach as incoherent, ill-thought-out and determined by "the loudest media voice at any particular time".

The criticisms are made in an extraordinary letter to the prime minister signed by the bishop of Leeds, Nicholas Baines, and written with the support of the archbishop of Canterbury, Justin Welby. Seen by the Observer, it describes the UK's foreign policy as so muddled and reactive that it is "difficult to discern the strategic intentions" of the government's approach to the region.

The letter follows widespread claims that Britain and the west have been slow to respond to unfolding events in Iraq as Islamic State, formerly known as Isis, has imposed its bloody rule across northern Iraq and swaths of Syria.

Cameron is taken to task for failing to develop an effective plan to tackle the spread of violent Islamist extremism from Iraq to Nigeria, where the militant group Boko Haram has terrorised the north of the country. "We do not seem to have a coherent or comprehensive approach to Islamic extremism as it is developing across the globe," the bishop writes.