I have only theories, I dont know , and I am a Brit too.
1.It may have something to do with the french word for box which is 'boite'.
2. My Oxford book of word origins says that a boot is the space for attendants on the outside of a coach, a receptacle for luggage on a coach, then it says 'mod F' (modified from French), which looks like 1(above) might be close to it.
Geek , it fascinates me too, maybe we can consult occasionally?
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HONK -if your keyboard has a horn