Brilliant. The tech info is new and welcome. I'd love to know who (in the UK) built the Essex and what it looked like. Probably Montgomery again. Luckily, again, for my purposes it doesn't matter too much.
There is another make we haven't mentioned: Villiers.
I've come across quite a few adverts for "Villiers Motor Cycle", seemingly new. I wonder, if you called into the shop to see the advertised machine, just what was written on the tank? There were also very many adverts for secondhand Villiers motorcycles, but that's just because "Villiers" was a better descriptor of a machine than the actual brand.
In the early days (particularly pre-WW1) in Australia it was very common for a locally-built machine just to have just the name of the engine on the tank: JAP, Precision, MAG, DeLuxe, Peugeot, Automoto, Buchet, King Dick, Sarolea, Fafnir, Minerva... so a machine with just "Villiers" on the tank would not be without precedent. Does the Police book list Villiers as a brand of motorcycle?
Leon