It's a 1953 Sun challenger (plunger) 197cc.
Aha. Can you turn your headlamp shell over, and find a Lucas number on it anyplace.
Does that tang shown on the Lucas rim have a suitable slot in your shell ?
I'd comment that a lotta Villiers powered beasties used Miller electrics.
My little Waratah/Excelsior, slightly earlier than your Sun, rigid frame, has a similar looking shell,
similar measurements. (no ammeter though). It has a Miller Lighthouse headlamp switch.
I've just been figuring out the connections.
Its got MILLER proudly emblazoned on the top of the rim.
https://i.postimg.cc/mDSbTYJb/Miller4.jpgI would think that Villiers Services are THE most likely folks to have the right rim for you.
As long as its Lucas.