Even before the Ayatollah came to power in 1979, Dad was often in trouble with the Shah for what he wrote. And very often his newspaper column would be a blank space because the Shah’s people had taken it out. The Shah was seen as a dictator, a puppet of the West. The Iranian people felt powerless under him. That’s why people like my father supported the Ayatollah Khomeini, who was then in exile in Paris. They thought if he took charge of the country, it would be given back to the people.

Dad was offered the chance to work in London, so we moved to Ealing and my brother Peyvand and I went to this lovely primary school. I hardly spoke any English, but I loved it. Going to friends’ houses, eating fishfingers… People seemed genuinely interested in where I came from. I felt very exotic. It was a very safe, English normality.

While we were in England, the 1979 revolution happened and the Ayatollah came to power. My father — like all the Iranians we knew — was overjoyed, and he decided to go back home to Tehran for a few weeks. Of course, he was still poking fun at the things he didn’t agree with, and when the Ayatollah imposed the hijab on women, my father wrote this joke about a man who had his wife flogged because she’d shown her hair to some dinner guests. The joke was, it was just that one of her hairs had fallen into the soup she was serving. The mullahs made a big fuss and my father was declared an enemy of Islam.

Iran is made up of a load of religions: the indigenous Zoroastrians, a huge Jewish community, Muslims and Christians. But these groups have always lived together in relative harmony. When Islamic fundamentalism was imposed on the country, everybody felt like the revolution had been hijacked.

My father was utterly, utterly heartbroken about all the fuss over the cartoon. Suddenly there were rent-a-mobs outside his office, baying for his blood. He had to flee down the back stairs into a car; then some friends just managed to get him onto a plane. Mum was in a complete state, because people were being executed willy-nilly. On the TV I could see my home engulfed in smoke and people beating their breasts. We were all relieved when my father made it back to England, but the death threats moved to England too. I’d pick up the phone and hear: “I will kill you, I will kill your father, and I will kill everyone.”

I was terrified. But Dad was this strong voice attacking the Iranian government, and they wanted him out of the way. It all reached a bizarre climax one day in 1984. Me and my brother were brought home from school early. There were two smartly dressed men in the house — from Scotland Yard — and Dad was skipping round the house going: “La la la, everything’s fine, children… but they’ve sent some terrorists to kill me. Isn’t that nice?!” Scotland Yard explained that a hit squad had been to Dad’s office in London and they’d found out where he was living. They were planning to shoot him between 8.15 and 8.30 as he drove us to school. The men from Scotland Yard said they were taking us to a B&B in Windsor — where nobody knew us.

Everywhere I looked I imagined I saw the Ayatollah’s head floating, waiting to kill us. But my dad just kept making a joke out of it. In fact, on our third day in Windsor the police came to see us. They were very angry with him. They’d told him that on no account was he to get in touch with anyone, but he’d invited all his friends over to the B&B. There are these brilliant photos of about 30 of us having a picnic down by the river — Dad was saying “cheers” to the terrorists for such a nice holiday in Windsor.

People might think my father was being very silly, but he wasn’t going to allow these terrorists to ruin his life. He still gets the death threats, even today. And I had a phone call last year saying I was going to die. I used to get very annoyed with my father. If he wanted to take these risks, fine — but did he have to put the rest of us through it too? As I got older, I think I finally began to understand him. For him, writing is more important than his life. Under the Shah, then under the Ayatollah, he lived with the constant threat of violence. But he won’t let anyone tell him what to do. He thinks: if we don’t stand up for our rights, what kind of world will we live in? He’s like a torpedo. Nothing can stop him.

Shappi Khorsandi’s show Asylum Speaker is at the Edinburgh festival, at the Pleasance Courtyard — the Attic, from August 3 to 28 (except August 14)