You have gazed upon the visage of Kate Middleton, or just above it, upon the sculptural clouds frequently affixed to her head, and had one of two thoughts. (1) Where can I get one? Or, (2) Kill it. Kill it before it kills you.

On this wedding-induced anthropological romp through Britannia, an American feels compelled to investigate a primal relationship: British women and their giant hats.

“This winter I probably bought six,” says Emma Yaxley, an advertising associate. She breezes through the John Lewis department store’s hat section, which displays little placards reading, “It’s a British Thing.”

“Six?!” says her friend Rachel Osborne. “I never — six?”

“You know. Berets, bobbles, Willy caps, Russians.” Yaxley plucks a wide-brimmed mauve hat off of a shelf. “Oooooooh.”

John Lewis has hats. It has “fascinators,” the headband explosions worn by Middleton. The store’s sales staff has coined a new term to bridge the gap: “hatinator.” Looks like a hat but attaches with a headband. This seems entirely like cheating. It also seems like something invented to go back in time and kill John Connor’s fedora, but this, perhaps, is another problem.

“It’s all come together at a most inconvenient time,” says Sue Simpson, the director of the lauded hat store Lock & Co., founded in 1676. “It” is the influx of hat demand, the unprecedented levels at which the British public is topping up. Easter is running into the Ascot races is running into garden party season. The beast of all hat occasions is the royal wedding, for which Lock & Co. is providing several hats. For one reason or another, an entire country must be hatted, sometimes for thousands of dollars apiece.

Americans seem to find this intriguing. “Carson Kressley is coming in later” to do a segment for “Oprah,” Simpson says.

Americans don’t do formal hats much anymore. Unless it is Easter Sunday or you are Lady Gaga, in which case your hat is probably made of something like police tape, or talons.

(Americans “don’t have [hats], really?” asks a perplexed customer in John Lewis. “But then what do you put on your — you just put nothing on your head?”)

In Britain, hats are ritualized. One could offer many explanations. It rains here, and hats are practical. It’s gray here, and hats are colorful. It’s classist here, and hats are difficult to fake well. In the sea of hats that recently attended Westminster Abbey’s Maundy Thursday services along with Her Majesty’s blue embroidered one, even a hat virgin could tell that some women were experts and some were imposters.

Let’s step away from hats for a moment and talk just about the British, and what we are learning about them through this wedding. The country has a reputation for stuffiness, but then it bestows upon the world “Crown Jewel Condoms” plastered with the faces of Will and Kate. Britons are supposed to be blustery and easily embarrassed, but they say “toilet” instead of “bathroom” — and don’t even blush!

Hats are, by definition, modest. But in practice they can be coquettish or salacious, making the wearer look even more bare than she would with a naked head. They are the wink at the end of a sentence.

The queen, who is notoriously remote, often wears hats that convey warmth and whimsy.

Hers are made by Rachel Trevor-Morgan, the queen’s milliner of five years. Trevor-Morgan has made the queen 48 hats, including a crimson one just in the news for nearly blowing off as she visited Prince William’s military base.

“I thought, ‘Oh no, her hat!’ ” Trevor-Morgan says. Later, she checked the weather and learned that winds had been 50 mph that day. It was not a wardrobe malfunction. “It was a nature malfunction.”

On a recent morning, Trevor-Morgan permits a reporter and photographer to visit her studio. Off a little alley called Crown Passage, it’s small and Dickensian with winding stairs leading to a small showroom. Two flights above that is her teeny workroom, where she hand-cuts and shapes each creation.

“If you’ve got a good hat on, people will notice you” for all the right reasons, she says.

She demonstrates how hats are formed and stiffened with glue, using tools inherited from the hatmaker who once taught her. She talks about finding the right hat, and how some women have to try on several before they get comfortable.

She is asked whether she can show some of the hats she is making for the royal wedding, and she demurs.

It wouldn’t be right, she explains apologetically, quite as if she has been asked to display the queen’s undergarments. Until she shows it off in public, a woman’s hat is a very private thing.