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Here is an anecdote that I recall reading as a child:

During World War II, the English found a way to smuggle microfilm past the German authorities. They sewed a hollow button to their jackets that could be unscrewed to reveal a tiny, secret compartment. Eventually, the Germans found out about this hiding spot, so the English came up with a new trick. They reversed the thread, so the Germans couldn't work out how to open the buttons.

Now, even as a child, I found this startling. Imagine risking your freedom based on whether a German guard slavishly followed "Lefty Loosy, Righty Tighty". As an adult, colour me skeptical.

So, my question is: Did this really happen?

But wait, where's the notability reference? Well, I am moderately sure I read this in "Great Imposters" (sic) by George Sullivan, but I no longer have access to the book. (Anyone?)

A more modern example of the claim comes from a 2013 Car Talk episode:

RAY: There were a lot of things they could have done. They could have applied some adhesive making them difficult to turn or they could have put some kind of a locking pin. But what they thought of was even better. They made the threads.

TOM: Left hand thread.

RAY: Exactly. So when the Germans twisted the buttons, they in fact didn't come off, they got tighter. And after they failed in a few attempts, they gave up on it because they just figured out, they're not using that trick anymore.

Their version says "Allies", rather than English, and I am nervous about relying on my memory on this point.

This claim appears to have been distorted from an original about hidden compasses, not microfilm. The compass version has been confirmed by the British Military intelligence officer responsible, Christopher "Clutty" Hutton.

According to Secret Britain: The Hidden Bits of Our History (2009):

When the Germans cottoned onto this, Clutty simply reversed the screw thread so that guards trying to unscrew buttons actually tightened them instead.

See also Official Secret: The Remarkable Story Of Escape Aids (1960) which is written in first person by Hutton himself:

In case I have inadvertently left the reader with the impression that our enemies were either stupid or blind, I should like to state quite categorically that those Germans who were responsible for running the prisoner-of-war camps were intelligent, shrewd and painstaking men, and that in time they intercepted nearly all of my various gadgets. The point was that each new device served its turn for a while and was of considerable benefit to escapers, but once it was 'blown', we either modified it or abandoned it altogether. When the camp searchers hit on the secret of our button compass, for example, we fooled them for an additional period by manufacturing it with a left-hand thread.

I also read almost exactly this as a child, circa 50 years ago, in Of Spies and Stratagems (1963) by Stanley P Lovell, who was the head of the US's Office of Strategic Services R&D division:

CAMOUFLAGE

As the number of secret agents sent into enemy lands by the O.S.S. increased, the invention and production of camouflaged items became an important activity. Disguised articles and concealed receptacles to keep messages secure from
enemy inspectors, [...]

Buttons on clothing were a favorite camouflage container. The top and base of the button were separated and a surprisingly commodious space was hollowed out. At first the top of the button was made to unscrew by turning to the left that is, counterclockwise. But the Germans soon found out about it, and all buttons on a suspected person's clothing were stoutly tested by turning them that way. If any one opened up, the Gestapo needed no further evidence to convict the spy.

We were about to abandon the item when one of my group suggested reversing the thread, so that twisting or turning to the left only served to tighten the assembly. Right up to Germany's surrender we never learned of one instance of this simplest of deceptions being discovered by enemy inspectors or police.

This mentions spies, messages (though not microfilm ) & Americans (though not the Allies specifically).

You can find this quote in Google Books. (I also just found a pdf online.)