A summary so far = this is a British make built 1919-21. It is mentioned in a well-known reference book but is not listed in a webpage of British defunct manufacturers.
It is NOT one of the following:-
Albert
Avro
Bean
Crossley
Dawson
Duplex
Hammond
HFG
Laurence-Jackson
Lecoy
Maiflower
Palmerston
Payze
Perfex
Richardson
Sports Junior
Thor
Zephyr