“If the Americans and the West are not prepared to do anything serious about defeating Isil, then we will have to find new ways of dealing with the threat,” said a senior Arab government official. “With Isil making ground all the time we simply cannot afford to wait for Washington to wake up to the enormity of the threat we face.”

The Peshmerga have been successfully fighting Isil, driving them back from the gates of Erbil and, with the support of Kurds from neighbouring Syria, re-establishing control over parts of Iraq’s north-west.

But they are doing so with a makeshift armoury. Millions of pounds-worth of weapons have been bought by a number of European countries to arm the Kurds, but American commanders, who are overseeing all military operations against Isil, are blocking the arms transfers.

One of the core complaints of the Kurds is that the Iraqi army has abandoned so many weapons in the face of Isil attack, the Peshmerga are fighting modern American weaponry with out-of-date Soviet equipment.

At least one Arab state is understood to be considering arming the Peshmerga directly, despite US opposition.

The US has also infuriated its allies, particularly Saudi Arabia, Jordan and the Gulf states, by what they perceive to be a lack of clear purpose and vacillation in how they conduct the bombing campaign. Other members of the coalition say they have identified clear Isil targets but then been blocked by US veto from firing at them.

“There is simply no strategic approach,” one senior Gulf official said. “There is a lack of coordination in selecting targets, and there is no overall plan for defeating Isil.”

Britain is moving closer to expanding its role in the war. The Government on Wednesday gave its strongest indication yet that MPs will be given a new vote on whether to bomb Isil in Syria.

Michael Fallon, the Defence Secretary, said it was “illogical” that British planes were able to hit extremists in Iraq but not across the border.

Any decision to bomb in Syria would have to be approved by MPs. In 2013, the Prime Minister lost a vote for British military action in Syria. However, Mr Fallon said: “It is a new Parliament and I think new Members of Parliament will want to think very carefully about how we best deal with Isil, and the illogicality of Isil not respecting the borderlines.”

Mr Fallon suggested that a bombing campaign could be mounted in revenge for the terror attacks in Tunisia if a link could be proved between the killer and Isil in Libya. Britain would only take military action in Libya “where we think there is an imminent threat, a very direct to British lives or, for example, to British hostages”, he said.

Senior Whitehall sources did not distance themselves from Mr Fallon’s comments but insisted there was no immediate prospect of military action.

The Telegraph understands that Mr Cameron is concerned that Labour might force the Government into another defeat over Syria.