As the Prime Minister vowed that Britain will not be involved in another war in Iraq, the Bishop of Leeds has criticised the government's inconsistency in its action against Islamic extremism.

Bishop Nick Baines wrote to the Prime Minister, with the support of the Archbishop of Canterbury and many bishops, critiquing the government's approach to tackling Islamic extremism around the world.

The most significant charge in the letter that was published in Sunday's Observer, was that the government's approach was reactive rather than strategic.

"It appears that, in common with the United States and other partners, the UK is responding to events in a reactive way, and it is difficult to discern the strategic intentions behind this approach," he said.

While the letter particularly addressed the threat from the Islamic State in Iraq and Syria, the Bishop of Leeds also raised concerns about the activity of groups such as Boko Haram in Nigeria. He said: "We do not seem to have a coherent or comprehensive approach to Islamist extremism as it is developing across the globe."

Bishop Nick commended the response to the plight of the Yazidi community, up to 40,000 of whom were stranded on Mount Sinjar in northern Iraq, but have since been helped by aid drops and air lifts. However he questioned the lack of response to the persecution of the Christian community by the Islamic State.

The bishop asked: "Does your government have a coherent response to the plight of these huge numbers of Christians whose plight appears to be less regarded than that of others? Or are we simply reacting to the loudest media voice at any particular time?"

He also commented on the lack of decision on whether to offer asylum to the victims of this persecution, noting that both the French and German governments have already done so.

Bishop Nick called for a greater commitment to protecting religious freedom generally.

The Bishop of Manchester, Rt Rev David Walker, told the BBC the government had a 'moral responsibility' to help Christians in Northern Iraq.

"We need to know what this government are prepared to do about those Christians in Northern Iraq, but also others for whom we have a moral responsibility, having intervened so substantially in that country just a decade or so ago," he said. "What's the government's bottom line? Are we prepared to take our share of those who've been displaced by what's happening at the moment and will need somewhere else to rebuild their lives?"

The Bishop of Coventry, Rt Rev Christopher Cocksworth, has raised questions in the House of Lords about Christians in Mosul. He called for Christians and Muslims to stand together against persecution.

"It's happening in a very, very extreme and deeply worrying and disturbing form as we hear about the ejection of Christians from Mosul and the intention to eradicate Christians in the area Isis seeks to control," he said in July. The same is happening in other ways with Shi'ites and terrible persecution and inhumanity. It is really important that Christians not only are deeply attentive to the plight of our brothers and sisters across the world who are suffering persecution as Christians but also we are attentive to wherever this right, this God given gift is being denied."

Writing in the Sunday Telegraph yesterday, David Cameron said that targeting the Islamic State was not just matter of foreign policy, but about protecting Britain from Islamic extremism.

"The creation of an extremist caliphate in the heart of Iraq and extending into Syria is not a problem miles away from home," he wrote. "Because if we do not act to stem the onslaught of this exceptionally dangerous terrorist movement, it will only grow stronger until it can target us on the streets of Britain."

The defence secretary Michael Fallon has said that British involvement could last for months. At present the military effort is limited to aiding the Kurds and sending surveillance aircraft over territory occupied by the Islamic State.

However the Prime Minister confirmed in an interview with the BBC today that there would not be a British military response on the ground – apart from facilitating aid deliveries as they have already done. He added that his priority was protecting Britain against the spread of Islamic extremism.