As I understand it the Footballers cap badge was commissioned by a dealer who is still with us. Very much within living memory and certainly not the 1920s.
I have never seen Middlesex Footballers cap badge, even a cobbled together one, with age or manufacture matching the 1920s. Certainly I’ve never seen a cap badge of the proportions shown in the catalogue.
The proportions do however match the rare Footballers sweetheart badge sometimes encountered -
https://www.britishbadgeforum.com/fo...light=football
Ditto the Leinsters. You’ll notice the bottom scroll on the Leinster cap badge has the feather tips poking down, on the sweetheart shown and badge in the catalogue the scroll had a flat bottom edge.
It’s possibly just coincidence.