A diificult one, this.
There’s no discernible detail in the dial, so there’s not much to pin it down. The only clue seems to be the lugs, which are fairly substantial compared to the case size. The lugs give the impression that they’re fixed, so maybe another clue. A reverse search doesn’t reveal much.
I might have suggested something like a Smiths Astral, many of which had small cases, but the lugs on these tend to be much slimmer.
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Even by the smaller proportions of the period, I would say the one in the photos is definitely a ladies watch - which might explain why he’s wearing two timepieces, and this one being on his right wrist.
It was very common for servicemen, especially pilots, to be given good luck charms by their female relatives and loved ones. Maybe this was given to him by his wife.
The strap on the left wrist appears to be much wider - I’m guessing the cuff is hiding something a little more appropriate, probably an Omega CK2129, a standard issued flight watch, given his bomber pilot status.
Great pics, btw
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