It’s official - I’ve got a really big head. Can I find a hat that fits?

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

Stay true to the cap’s sporting heritage with the official supplier of licensed baseball and American football team hats, available in up to a brow-busting 63.5cm.

BUY: 59Fifty low profile baseball cap, £35.95, at Village Hats

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Sealskinz beanie hat

Function meets understated winter style in this waterproof beanie from the British rain-dodging specialist. The XXL will keep the biggest heads drier and toastier than a bag of KP.

BUY: waterproof cold weather roll cuff beanie hat, £35, Sealskinz

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Luca Faloni baseball cap

Channel your inner dressed-down finance bro/prince (Wills is a fan) with a linen number from the Italian label whose take on quiet luxury is everywhere. Bands are elasticated to fit up to 60cm.

BUY: coral linen baseball cap, £120, Luca Faloni

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Varsity baseball cap

Founded by Norwegian brothers with larger heads, the XL from this baseball cap specialist will cosset heads up to 62.5cm in diameter. The summer Seaqueal is squishable and breathable.

BUY: pine green Seaqual legacy soft cap, £65, Varsity

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Under Armour cap

It’s fitting that a brand founded initially to clothe hulking American footballers should offer hats for the fattest heads. UA’s stretch-fit XL/XXL caps are designed for heads of up to 65cm.

BUY: men’s ArmourVent stretch fit cap in camel/coyote, £25, Under Armour

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Classic Max-Cap

You won’t find larger hats than those at max-cap.co.uk, an online shop founded by a man with a big nut. Its understated XL caps, which come with small price tags, size up to a huge 68cm.

BUY: classic Max-Cap, £18.50, Max-Cap

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CP Company bucket hat

The Italian streetwear specialist known for its hoodies with built-in goggles does a technical bucket hat, including an XL, in its recycled Chrome-R fabric with a goggle lens detail (if you know, you know).

BUY: black Chrome-R bucket hat, £150, CP Company

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Ralph Lauren bucket hat

RL’s Polo Bear character, born in the early 1990s, adds a nostalgic touch to its twill navy bucket hat. The L/XL will fit large but not massive heads (there’s no stretch in a bucket).

BUY: navy Polo Bear twill bucket hat, £89, Ralph Lauren

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Moncler bucket hat

The Italian luxury brand has leaned into the bucket renaissance with hats featuring in its collabs with Alicia Keys, as well as a furry number designed by Jay-Z. This pixel-print offering comes in XL.

BUY: patterned reversible bucket hat, £325, Moncler

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Jacquemus baseball cap

There’s a lot going on in this cap from the youthful French label, but if you’ve ever dreamed of a hat made of denim with a furry fringe and a drawstring, look no further. Sizes up to 62cm.

BUY: frayed baseball cap, £105, Jacquemus

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Lock & Co Qest panama hat

If it was good enough for Nelson and Churchill … The world’s oldest hat shop has kept up with the times and serves heads of up to 65cm. This timeless Panama is handmade in Ecuador, and proceeds from every sale go to Qest, a charity that funds the training and education of young British craftspeople.

BUY: Qest panama hat, £345, Lock & Co Hatters

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Dents flat cap

The legacy London glover does a fine line in affordable hats, including this classic flat cap in check tweed from the historic Abraham Moon mill in Yorkshire. Sizes up to 62cm.

BUY: men’s Abraham Moon check tweed flat cap, £49, Dents

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Barbour bushman hat

You don’t have to be walking a labrador across Richmond Park to embrace the styling of this foldable felt number, but nor would you look out of place if you were. Available up to XL (61cm).

BUY: crushable bushman hat, £59.95, Barbour

Selection by Sam Deaman, the Guardian and Observer’s fashion assistant