When the England test captain, Ben Stokes, wore a bucket hat with the Three Lions crest embroidered on the front at the first day of the men’s Ashes last week, it brought almost as much attention as the Test match itself. The hat, known as a titfer, cost £25. On Twitter, he became known as “Bucket Hat Ben”.

A few days later, the sight of Pharrell Williams on the Pont Neuf over the Seine taking a bow after his debut collection for Louis Vuitton in a snug-fitting baseball cap, was a stark contrast. It speaks to a battle going on from the grass of Edgbaston to the catwalks of Paris, and in towns and cities up and down the UK – that these two styles of hat are battling it out to keep heads protected and noses in the shade this summer.

Both are hugely popular. The Manchester City footballer Jack Grealish wore a patterned bucket hat after winning the treble, while the red carpet has this year had more than one suit worn with a baseball cap – for instance on Bad Bunny at the Grammys. At John Lewis, sales of caps and summer hats are up 30% on last year.

The jostling for headspace speaks to the tribal nature of hats, which are “seen as signifiers”, according to Ben Dalrymple, the managing director of Lock & Co Hatters, the institution to thank for inventing the bowler hat. “Team allegiances, vintage looks, high fashion, casually cool or even a uniform – hats tell a story about the wearer,” he says. And as much as they are “designed to be protective, their wearers are fiercely protective of them, and what they represent”.

“They are often intrinsically linked to a certain crowd,” says Ben Phillips, the head of e-commerce at Drake’s, a Savile Row “maker and haberdasher” that sells a number of elevated caps apt to be worn atop suits – noting that “we all know a ‘bucket hat guy’”. Phillips says: “Once you find one that works for you, you stick to it. It’s a calling card for those in the know.”

This is nothing new. But who is wearing which hat might not be as straightforward as it once was. Bucket hats started life at sea. “The bucket hat originated in the late 19th century/early 20th century as a very practical form of headwear for mariners and fisherman, particularly in Ireland,” says Dalrymple. They would have “originally been made from coarse sheep’s wool – the lanolin within the fibres making the bucket hat water-resilient”. Shifting into canvas, the style became popular more widely “for keeping the sun off and being easily packed in a suitcase or a jacket pocket”.

They became fashionable in the 1960s, according to David Long, the author of The Hats That Made Britain: A History of the Nation Through Its Headwear, “when seemingly anything new and unusual was hip”. Popular with hip-hop artists such as Run-DMC and LL Cool J, latterly their currency has “grown out of festival culture” – they became synonymous with Britpop in the 90s, when the Gallagher brothers and Damon Albarn were rarely seen without one.

For a hat that has become more synonymous with high fashion, it will not be surprising to learn that baseball caps started life on the sports field. “It was originally known as the Brooklyn cap in the late 1800s/early 1900s, with its origins traced to the local baseball team,” says Dalrymple. But they have become just as apt for the front row of fashion shows or the boardroom as for the pitcher’s mound.

On television, Succession’s billionaire Roy family have been wearing conspicuously sloganless baseball caps in a subtle show of power – and anonymity. While in recent years they have become the site of slogans – part of the nerd merch movement that lets wearers signal highbrow literary tastes on their everyday garments. It is telling that Novel Mart, a cult merch cap-maker, started out with slogan baseball caps embellished with the word Negroni that went viral – but has now moved into bucket hats, with the word Paloma becoming the latest bestseller.

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With the resurgence of baseball caps, Phillips has even found “dyed-in-the-wool sartorial customers” opting for them. A cap worn with tailoring can, he says, instill “a casual elegance in juxtaposition, a mixing of high and low that when done right suggests you’re going somewhere better, later”. Judging by Grealish, the bucket hat suggests the party has already started.

So which style is winning this summer? Glastonbury, which is entering full swing, will be an ideal test site for where the battle of the hats is headed next.