It was early evening when the motor conked out, and we were stranded. We started to shout in the hope that somebody would hear us; we knew the sound could travel because of the water being very flat and calm.
Suddenly, as if out of nowhere, there was this disturbance in the water. I remember everyone initially thought it was a dolphin, but it wasn't leaping in and out of the water, and before long we could see this stiff grey fin moving purposefully towards us.
It then circled around our rowing boat, and I remember my father saying: 'Well, I think that's a shark . . .'
And then this monster started bashing our boat, which began rocking from side to side, and everyone got hysterical. We were just terrified because the boat was by now rocking so much we thought we were going to be tipped into the water and chomped up by this thing. I remember assuming that we were going to die. My mother was screaming, and father was shouting obscenities at this thing, which he was to bash back with one of the oars. I had never seen my parents in obvious terror before, and that's something which never leaves you.
For the longest time this thing kept circling around us, and ramming our rowing boat, while Dad continued fending it off, stabbing at it with his oar, which was probably the worst thing to have done because it must have made the beast even more livid than it already was.
My mother clutched the three of us around her. I remember she had a voluminous navy blue towelling robe, with huge starfishes and sunflowers on it, and us three kids gratefully huddled together inside it.
Eventually, people in a fishing boat heard us screaming, and came alongside, and a fisherman tied our boat up to his. He was very careful, or he seemed to be, and he and my father handed first us kids, and then mother, through to his boat, and our rowing boat was towed behind.
As soon as we were in the fishing boat there was this almost hysterical laughter, and I remember feeling very cold, and being unable to stop shivering.
Our story went back to the town, it spread like wildfire, everybody knew about it, and people talked about it endlessly. My father was regarded as a bit of a hero: Dad the sharkbasher. If he'd caught the thing, then I suppose he would have been completely heroic.
We all talked about it incessantly, too, and probably made out we were far braver than we were. And there was lots of re-enactment, I remember that we made mud pools, one of us would be crawling along, playing the shark, and the others screaming and shouting: 'Kill the shark]'
Two or three weeks later, near the end of our holiday, the shark was caught by one of the local fishermen, and put in the main square for people to go and see. It was real gargoyle time. This thing was strung up on a pole, and it looked horrific because they had slit its stomach open, all its innards had fallen out, and all the intestines were lying in a pile underneath it, with flies buzzing around. Everybody came to see it, and people took pictures.
We all touched it. There's no texture quite like a shark; its skin is very abrasive, like leather with steelwool attached to it. If you ran your hand hard against it, you would suffer the equivalent of stinging nettles.
My daughter likes to hear this story a lot. She's five now, so she likes monstrous or horrific tales. She hasn't seen Jaws, I'm keeping that for a few years' hence - besides, I nearly had a thrombosis when I saw Jaws - that grey fin moving relentlessly through the water, coming towards you . . .
I suppose I do go on about it. I'll come across friends I haven't seen for 20 years, and the first thing they'll say is: 'Still going on about that shark?' So I think it must have really affected me.
I've never since had a closer sense of feeling I was going to die, and so critics, job rejection, everything else daunting in life seems less frightening in relation to that.
Richard E Grant is an actor.