Now I am NOT going down the "Villiers Inustrial Engines" rabbit hole, but I will admit there is one! As Reg says in his memoir, P&R Williams were a big part of the Australian end of the business, in the 1930s, with a gap for the war, then 1946 into the early 1950s.
I suppose the 98cc Villiers Midget in the Ransome lawnmower is akin to the engine in the 98cc Waratah of the time? On second thoughts, don't answer that!
Leon