For a neglected section of society, few other phrases are so divorced from reality as “one size fits all”, when sewn inside a hat. A more accurate version would read: “It makes no economic sense for us to make multiple versions of this product.” Or: “We don’t care about people with really big heads.”

I am a person with a Really Big Head (RBH – I’m making that a thing). And you know what they say about guys with big heads? Big hats. Especially if they’re also bald and don’t want to get skin cancer. Yet for most of my adult life, summers have involved a tragic search for a hat that fits.

This year, I’m ramping up my quest. As a middle-aged dad, I tend to reach for a baseball cap. I would probably go for an outdoorsy Patagonia number, but such “one size” offerings either won’t fit or they leave behind a headache and a dent. After a day in the sun, I look as if I’ve head-butted a shopping trolley.

I measure my head’s circumference, just above the ears: 61cm. Good head-girth data is scant but what evidence there is suggests I do have a large head, but also that all bonces are bulging as populations grow taller and fatter.

One study at the University of Tennessee – measuring the skulls of 1,500 American men born between 1825 and 1985 – revealed a head height increase of 8mm (they didn’t measure girth). A smaller 1992 survey of British men revealed an average head girth of 54-60cm, depending on height (at my height, 61cm is in the 90th centile for girth).

I remember my grandfather, who had the same problem, bodging adjustments to his straw hats. Perhaps inspired by him, I once unpicked the elastic brim of an “XL” cap I’d bought from an obscure Amazon supplier to loosen it. It helped, but I’d have to sweep fraying threads into the hat before plonking it on my head.

When I lost that hat, I went nuclear and bought the XXL. It could have housed a family of squirrels, and swivelled on my head when I shook it. So I looked for a specialist, ordering a navy hat from max-cap.co.uk (“large hats for large heads”). My Max-Cap fitted pretty well, but then took flight from a Greek speedboat. Since then I’ve put up with another unpicked Amazon purchase and a dented head.

Determined to do better, I start my search at John Lewis. Mark Lewis, a stylist there, also has a big, bald nut. “I’ve tried so many styles and I’ve kind of given up,” he says. He likes bucket hats, or timeless fedoras for smarter occasions, regardless of girth. “But I think baseball caps are easiest,” he says, partly because of their relative stretch or adjustability.

We’re living in a cap age; the lazy fallback is having a moment. From a statement of quiet luxury – see Kendall Roy’s £440 cashmere Loro Piana example in Succession – to a street-ready sun-shade (see the likes of model Kendall Jenner in a budget Yankees cap). Cap sales are up 22% on last year at John Lewis, and they’ve even graced catwalks for Celine, Hermès and Dior. But that doesn’t help me if they don’t fit.

Wondering if head shape rather than size might be my issue, I visit Maxwell Newman, a 28-year-old DJ and fitter at Lock & Co Hatters, which has had the same central London store since 1765. Nelson came here for his bicorne and Churchill for his bowlers.

“You are seven and a half, sir,” says Newman, who is, under his chic beret, yet another bald guy with a big head. Hatters use an archaic British scale; Newman confirms I’m 61cm. He’s about the same and says that while I’m definitely XL, he often sees bigger heads and occasionally reaches for a 65cm, the biggest hats in stock.

Newman suspects I have “a very long fitting”, which is a polite way of saying I have the profile of an alien from Alien. “I would imagine that hats are tight at the front,” he adds.

Newman pushes a conformateur over my head. The 19th-century French device, which looks like a torturer’s top hat, creates a one-sixth size outline of my head on a piece of card. Mine has an elongated Russian-doll shape. Dozens of these cards have been signed and framed in the shop, ranging from neat oval (Franklin D Roosevelt) to amorphous slug (David Walliams). I note that I have the head shape of Colin Farrell and the girth of Pierce Brosnan, which is nice.

The card goes into another contraption called a formillion to create a hardwood replica of the head, which can then be pushed into steam-softened top hats or bowlers. I’m not in the market for a topper so Newman talks me through Lock’s range, which now includes baseballs and buckets as well as fedoras, panamas and baker boys. I try on a few in my size, marvelling at the feeling of hats that fit just so.

I lean towards the baseball caps, although they’re a bit posh for me and at least £125. But something clicks when Newman hands me a £245 straw St Louis trilby, which is Lock’s bestseller. It has a classic shape and, though definitely semi-formal, is also slightly rustic. I’d never considered the need for a smart hat, but could this be it?

While I weigh up my options, I continue my search for an everyday baseball cap rather than a statement piece. It is in the unexpected location of Oslo that I find what I am looking for. As I’m strolling through the airport, a store called Varsity, which sells only baseball caps, turns my fat head. Hearing of my predicament, the sales rep reaches for XLs in various styles. They fit perfectly.

Sebastian Adams, who’s 42, co-founded the boutique chain in 2013. As a fellow RBH holder, he ensured the inclusion of a proper XL. He later tells me these hats account for 8% of sales. “But I believe that these customers are loyal, because they’ve found it difficult to find nice headwear that fits,” he says. I cough up £60 for a cap (in coward’s navy, of course) and have worn it all summer. It caresses rather than grips my head, and I sometimes forget it’s there. After years of compromise, I feel like my hat quest is over. But I keep thinking about that fancy trilby. Does the price include a new wardrobe and flights to Capri?

12 hats for big heads

New Era cap