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I see no great significance to the kid's hats being worn by the gang, in my "greaser" days we would ride to Brighton or Southend and many of us put on those things for a laugh.
I'd just like to clarify that "Teddy Boys" referred ONLY to teenagers who had drape jackets in often vivid colours with velvet collars, drainpipe trousers and crepe soled suede shoes (known as brothel creepers). They also had a Tony Curtis hairstyle with a DA at the rear, held down with lashings of Brylcreem!
There were Teddy Girls as well with drape jackets, pencil skirts and beehive hairstyles.
Ted's would NEVER ride motorbikes, they all aspired to big Yank Tanks but usually settled for Ford Zephyrs or Vauxhall Crestas.
happy memories!!
Come on lads, bags of swank!

Great explanation, thanks.

Enlarging just a bit on the previous comment, I noticed a young boy wearing the same kind of hat in the 1960 film version of The Entertainer. It was set at an aging, Victorian era seaside pavilion, possibly Brighton, and the boy is with his parents, looking at posters advertising the naughty comedy act of Archie Rice at a music hall. I'm pretty sure there's a stand in the background of one scene, where you can see those same hats for sale.
I've always thought those hats looked pretty strange on leather jacketed hoodlums, loitering around the boardwalk, waiting for a chance to mug someone. Perhaps it was intentional on director Losey's part, to suggest that these hoodlums were actually just mixed up kids? Or they thought it made them look innocent and out for fun, instead of planning violent crimes?
And when he crossed the bridge, the phantoms came to meet him

They were typical hats that you would buy at a seaside town - a typical seaside feature. This is Weymouth, Dorset.
In the film the yobs are called "teddy boys". At the time that phrase meant any young yobs, not just people in 50s style clothes. The term died out a couple of years later with "mods and rockers"

They were children's party hats, the type made of rough pulp compressed into cardboard, similar to that used for egg boxes - a staple item at least until the 1980s..
=:o)

Thank you.

pdmh,
I gather it was 'cool' at the time for tough guys to partly dress like dorks.
Even in the 'Beach movies' of the period, the gang members often wore silly hats or helmets.