Slip! Slop! Slap! It’s an Australian mantra. In the fierce sun here, everyone is exhorted to slip on a T-shirt, slop on some sunscreen and slap on a hat. While I can do the slipping and slopping, the slapping is a problem — hats don’t fit me. I have a really big head and it always looks as though I’ve accidentally picked up a child’s hat and am trying it on for humorous effect.

I’m deeply embarrassed by this — it seems so unladylike to have an enormous head — but I try not to let on I care. “All the brains,” I say mock-ruefully, when friends make me try on hats and then guffaw. “Yup, I need a huge head for all the brains,” I say, beaming broadly because it’s so incredibly funny that I’m the Elephant Man’s sister. Inside I’m dying. It’s an affliction normal-headed people could never understand.

Over the years, I’ve tried on innumerable hats and they never fit. Shops tend to label women’s hats as “one size”, for which I read “Tiny”. Occasionally, they come in Small, Medium and Large, which appear to be for heads the size of golf balls, tennis balls and footballs, respectively. None are ever for heads the size of medicine balls.

I’ve tried men’s hats and been similarly disappointed. Occasionally, a flat cap fits but as Dinny from Glenroe is hardly a fashion icon, I’ve desisted. Rarely, some other sort of man’s hat has fitted, but been deeply unflattering. Anyway nobody, with the possible exception of Helena Bonham Carter, pairs a pretty summer dress with a Russian military hat with furry ear flaps.

It’s particularly frustrating because I’ve always thought of myself as a hat person. I could carry off a hat, if I could find one large enough. Every time I see a girl in a beret, a cloche or a floppy straw number, I think wistfully: “That could be me, if only milliners dared to dream big.”

Over the years, I’ve come to accept hatlessness as my cross to bear, but now I’m in Australia and it’s practically a criminal offence to go bare-headed. I’m asked constantly why I’m not wearing a hat and warned of the dire consequences of sunburn and sunstroke.

So I’ve tried on dozens since I got here. Almost none have fitted. A bile-green bucket hat I found in a surf shop did fit, just about. “What do you think?” I asked my friend delightedly. “Weeell,” she said, her face contorting in that way faces do when people are desperately trying to think of something nice to say and can’t manage it. I looked in the mirror and saw Victor Meldrew. I didn’t buy the hat.

Then I stumble on Strand Hatters, a shop just off George Street in Sydney, which sells every sort of head gear imaginable, even fezzes and pith helmets. My pulse quickens. I go in, trying to look casual. Gingerly, I pick a Panama hat from a shelf and glance at the label. It’s an extra-large. I put it on. It fits. Onlookers will assume I’ve mugged an elderly European gentleman for his hat, but I don’t care. And if this one fits, maybe others in here do, too.

I take off the Panama and put on an extra-large stetson. It fits. I try an extra-large Akubra, the Australian bush hat. It fits. It’s good to know that if I ever want to pass myself off as a cattle rancher, I can. The extra-large Homberg fits. I tip it down over one eye and do my best Bogart face in the mirror. I’m not sure when I was last this happy.

As I dart giddily about the shop, a thought occurs to me. Although this is a men’s headwear store, I might actually find a flattering hat here. One that looks as though I chose it for its fashionability rather than its gargantuan size.

I enlist the help of the shop assistant, a polite young man, and explain how I have a huge head. He is sympathetic and pretends he can’t tell this just by looking at me. “What about this one?” he says, picking up a trendy pork pie hat. “It’s a 61.” This means nothing to me, but when I try the hat, it doesn’t fit.

“Have you the next size up?” I ask brightly. He looks embarrassed. “Normally, anything above a 61 is a special order,” he mutters. I force a tight smile. “Never mind,” I say.

He’s not defeated, however, and suggests I try a woven seagrass trilby. It fits. Not only that, it looks hip. I’m both triumphant and vindicated. I knew I could carry off a hat.

Once my excitement dies down, I admit it’s actually a little tight. “That’s okay, I can stretch it on this,” he says, pointing to a medieval-looking contraption on the counter. He puts the hat on it and cranks a big handle. After five minutes or so, I try it again. It’s less tight, but not perfect. “If we stretch it overnight, it should be ideal,” he says. So I hand over AU$49.95 (€24.99) and leave my hat to spend an uncomfortable night on the rack.

Tomorrow, finally, I will be able to participate fully in the great Aussie tradition of slipping, slopping and slapping. Every day, in some small way, I’m a little less like a tourist.

Times Recommends

• 'New York has lost its edge'
• Copenhagen will fail – and quite right too
• More than 17,000 new underwater species found