These cards often still come up for auction in their original collector book. You've probably seen them if you searched on eBay. I suspect these books were cheap and/or promotional as I have never seen a pre-war sports set that is so readily available in a completed form as these. I have my doubts as to whether these cards came in individual cigarette packs. I'd guess that they were just something one could pick up in the book from their local tobacconist but that's merely a guess. I'd say they're in so many US collections because they are so cheap and they actually make up a pretty nice set. I don't think Churchman's was available in the US at the time. I bought my set shipped from the UK for about $20. I suspect many other collectors did the same. They include many US star boxers, some even in their prime. A lot of US collectors would have interest. I would also say that no other set demonstrates the fallacy of the psa price guide as this one.
Sorry these are all guesses. Being that there's a collector culture in the UK for "cigarette cards" I'd say maybe try to find a contact. This guide is published in the UK and might be a good start.
https://www.amazon.co.uk/Cigarette-T.../dp/1906397163