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The Beatles were a pop and rock group from Liverpool, consisting of George Harrison (1943-2001), John Lennon (1940-1980), Paul McCartney (born 1942) and Ringo Starr (Richard Starkey – born 1940).
—Cf. the adjective grotty, the noun John Lennon spectacles, the phrase to be more popular than Jesus, and the nouns Beatlemania and Beatledom.
The noun Beatle boot (also Beatles boot) designates a type of ankle boot usually worn by men, typically having a leather upper, Cuban heel, sharply pointed toe and a zip or elasticated gusset at the side.
Boots of this type were popularised by the Beatles in the early 1960s, and are primarily associated with the fashion of this era.
The noun Beatle boot occurs, for example, in the following from The Wish (from the 1998 album Tracks), by the U.S. singer-songwriter Bruce Springsteen (born 1949):
Well, it was me in my Beatle boots, you in pink curlers and matador pants,
Pulling me up off the couch to do the twist for my uncles and aunts.
These are, in chronological order, the earliest occurrences of the noun Beatle boot (also Beatles boot) that I have found:
1-: From The People (London, England) of Sunday 20th October 1963 [page 13, columns 1 & 2]:
—Note: The use of the noun beetle-crusher in this article is interesting, since the name Beatle is an alteration of the noun beetle after the noun beat:
WHAT WERE THEY ALL QUEUEING UP FOR?
Answer
The Saturday ration of Beatle BootsThe queue began at 6 a.m. The doors opened three hours later. And the rush was on. The rush to buy a pair of boots.
Not just any old boots, mind you. Not the beetle-crushers dad used to wear.
These were very special boots. Boots with thick Cuban-style, three-inch high heels. The kind of boots (inset) worn by those Merseyside marvels, The Beatles, and on sale in London’s Drury Lane on Saturday mornings only.
The boys who hit the top charts with “the Liverpool Sound” have started the biggest male craze for years.
Said 18-year-old Peter Bellingham, one of dozens who queued yesterday for a pair of Beatle boots at £3 15s.: “I couldn’t call myself a real Mod (modern) until I got my Cuban heels. I was only a Mid” (halfway to a Mod!).
That, of course, explains everything.
FOOTNOTE for would be Mods: The Cuban-heel boots were designed as a joke by a craftsman with a firm which specialises in theatrical footwear. Then The Beatles bought a pair each.
This photograph of Beatle boots is the above-mentioned “inset”, in The People (London, England) of Sunday 20th October 1963 [page 13, column 1]:

2.1-: From And now the Beatle boot is coming…, an article about the 1964 spring range from James Boylan & Son Ltd., shoe-manufacturers in Emyvale, County Monaghan, published in the Evening Herald (Dublin, County Dublin, Ireland) of Tuesday 29th October 1963 [page 11, columns 1 & 2]:
One must agree the fashion interest is there, looking at the stylish shoes destined to adorn the feet of young Irishmen—and Englishmen—next spring and summer. I mention Englishmen because this firm is having tremendous success exporting shoes to Liverpool Manchester, selling in some of the biggest stores.
Most sensational item in the new range, and due in the shops early in December, is the Beatle boot, inspired by the Liverpool pop-singing group.
Boylan’s are marketing this in brown mock crocodile, studded with a gilt motif and elastic-sided, and also in black calf. The Beatle boot, like the lizard-trimmed black cowboy boot, features the stacked Cuban heel—apparently the current fad of the pop-singing idols.
Will it sell here? “I have no doubt at all,” says Mr. Boylan. “It will be a winner.”
[…]
Most of these new styles will be in the shops early in the new year, but for the boys who cannot wait, there is every prospect of the Beatle boot being in the shops well before Christmas.
2.2-: From the Irish Independent (Dublin, County Dublin, Ireland) of Tuesday 29th October 1963 [page 5, column 7]:
New ‘Beatle boot’ out shortly
“Irish Independent” ReporterStriding into the male fashion world during the next few months will be the “Beatle Boot,” named after the recording group, “The Beatles.”
Manufactured by James Boylan Fashions shoes, the boot, Cuban stacked heeled, comes in a variety of colours and finishes. All styles have narrow chisel toes and are close fitting, with elastic sides. James Boylan Junior, Marketing Director of the firm, says that the boots should be in the shops just in time for Christmas.
3-: From the Cumberland Evening News (Carlisle, Cumbria, England) of Wednesday 30th October 1963 [page 8, column 4]:
Having had time to reflect on the past week-end’s Beatles ticket queue scenes a reader, who wishes to be known simply as “Now Cubic” (square to you!), Abbey Town pens:
No doubt you heard them say “How Do You Do It?”
It’s a pop-picked phrase that’s going all around.
Some deplore it, most adore it, others boo it,
But no one can ignore the “Mersey Sound.”
Quite recently in Carlisle they were queueing,
With ready cash to buy a precious ticket,
Some oldies said: “Tut, tut, what are they doing?”
While others preached: “By gad, sir! That’s not cricket.”
[…]
Though you don’t rave for Beatle boots and leather jackets,
Or the way this boisterous foursome dress their hair,
And that “sound” be simply nothing but a racket.
Please get with it, friends, get with it and be fair.