I went recently but didn’t realy look for scooters,only British scooters I can think of are Triumph Tina/Triumph Tigress/BSA Sunbeam/DMW Deemster/ and the best British one built in my opinion the Velocette Viceroy
The BSA Sunbeam 250 and Triumph Tigeress 250cc scooters had a twin cylinder electric start air cooled motor, a few specials have been made using this engine, it can be shoehorned into Bantam and Tiger Cub frames.
Honda NC750 Manual
VESPA GTS250
Royal Enfield HNTR 350
Honda Forza
Also option of 175cc 2 stroke motors on the BSA/Triumphs.Good point regarding the engine fitting into a Bantam frame,missed opportunity for BSA maybe.It wasn’t one of their own engines though was it??
The 175 was a development of the Bantam engine anyway. I think the 250 twin was an Edward Turner design, in-house Triumph. Foot change via a rocker pedal through the footboards if I remember rightly. Looked great and went well but wasn't very reliable.
2009 Burgman 400 in sunny Perranporth
Always seek the happy medium - she's out there, riding her scooter.