Arriving in Erbil, you don’t feel you are in Iraq, but another country altogether, which is what the Kurds would like. The city’s outer ring is shiny and new, a touch of Dubai in the smooth highways and glittering hotels. A London property developer told me he had made a 40 per cent return in Erbil. He was Jewish, too — might have been a different story in Baghdad. The Kurds are proud of their embryonic capital: open for business; tolerant of all faiths; you can even get a drink. But two weeks ago Erbil was seized by panic, the Islamic State almost at the gates. A diplomat told me the security forces were on the point of fleeing. The US airstrikes steadied nerves.

It’s been suggested the Kurds have been living off their reputation for military prowess. It is 20 years since they fought a serious battle, except among themselves. Peshmerga recruits are no longer hardy mountain boys who grew up with a rifle over the shoulder, said one commentator: they know weapons only from Call of Duty. In several towns where the Islamic State advanced into Kurdish territory, the defenders simply ran, officers first (including some with ‘quite famous names,’ according to my diplomat friend). One town, Makhmour, was recaptured after US airstrikes began. We watched the reinforcements taunting the townsmen with accusations of cowardice. Stung, the men shouted back: ‘We didn’t bend our knee to Saddam — and we won’t surrender to the Islamic State.’

During the Erbil ‘wobble’ the Kurds deployed a very capable Special Forces unit. Its commander, Polad Talabani, grew up in Beckenham, south London, with his brother Lahur, now head of Kurdish intelligence. Both greet you with a cheery Estuary English ‘All right mate’. Polad was training to be a motor mechanic at Bromley College before deciding to return to his homeland. He told me, though, that he had spent his early childhood in the mountains and that his fifth birthday present was a pistol. The new Iraqi prime minister, Haider Al-Abadi, also has strong British connections. The story is that he used to ‘fix the lifts’ at Bush House, former home of the BBC World Service. Not quite. He did a PhD in electrical engineering in Manchester and later joined the lift company that had the BBC contract. Still, a colleague swears she saw Dr Al-Abadi in overalls, tinkering with the lifts.

We leave Iraq for Syria, crossing the Tigris on a pontoon bridge put up by the UN. Little groups of exhausted refugees from the Yazidi religious minority wait to cross the other way. We’re all going through Syria from one bit of Iraq to another because the Islamic State has blocked almost every road. Once over the border, signs point the way in Kurdish, Arabic and Aramaic. A plethora of Syrian Kurdish armed formations are in charge here: the HPG, the YBS, the YPG and the group that used to fight the Turks, the PKK. All are scornful of the Iraqi Kurd Peshmerga. They say they fled leaving the Yazidis to their fate. The Iraqi Kurdish forces, meanwhile, are drawn from the erstwhile rivals, the KDP and the PUK. The Kurds are complicated.

A Syrian Kurdish officer — wearing traditional baggy pantaloons and sash — gives us an escort to Mount Sinjar, which is back in Iraq. More than 100,000 Yadizis fled over the mountain. Some are still making their way out. We drive across desert, threading our way between Arab towns and villages held by the Islamic State. Our escort takes a wrong turn and slams into reverse, a jihadi checkpoint ahead. Even in a vehicle, the heat is intolerable. The refugees walked 40 miles in more than 50˚C. A female Kurdish soldier tells me her job was simply to hold the hand of the dying after they had fallen by the wayside.

Eventually, we are sitting on top of Mount Sinjar with about 60 Yazidi men. Shade comes from a tarpaulin bearing the slogan ‘From the British people’, having been dropped by the RAF the night before. The talking is done by an elderly Yazidi in a brown felt hat shaped like half an eggshell, four plaits of grey hair hanging down. We discuss the Yazidis’ belief in the ‘Peacock Angel’, who defied God and was cast out of heaven, to return after begging forgiveness. In Muslim theology this is Lucifer — that’s why the Islamic State persecutes Yazidis. More of the Yazidis’ ways are explained. Yazidi priests are celibate, though self-castration has (mercifully) died out. Yazidis don’t eat lettuce. That dates from a massacre by the Turks that took place in a lettuce field, Yazidi blood soaking the leaves.

A couple of days later we walk into a restaurant in Iraqi Kurdistan. A table of extravagantly moustachioed men offer to buy our dinner, having mistaken us for Americans. ‘Thank you for bombing our enemies,’ they say happily. That evening US airstrikes forced the Islamic State to abandon Mosul dam, though the jihadis furiously deny it on Twitter, their preferred propaganda medium. Twitter has started to close some IS accounts. A furious jihadi tweet, translated from the original Arabic, says: ‘Pass this to the Twitter Admin, the dog. Either leave us to tweet as we wish, or we will blow you up. You have been warned.’ The Arab villages around the dam are empty, some of their men having joined the losing side of the battle. The Islamic State is not purely some foreign blight but something which has grown from the soil of Iraq, a fact of some importance for any country contemplating an open-ended bombing campaign. I asked the Kurdish mayor of Makhmour — briefly conquered by the jihadis — if he could ever again live with those of his Sunni Arab neighbours who’d sided with the Islamic State. ‘No, of course not,’ came his answer, quick as a flash. Step by step, then, Erbil is becoming the capital city of a country, and not just of a region.