I suspect you already have it, but this is what Tony Buttler says in the latest BSP:1 edition (re: the Supermarine Type 543); "The drawings and performance were based on two Bristol BE.15 engines mounted side-by-side; this was the largest axial jet available with the highest possible degree of reheat, but the alternatives were an Avon development, the Sa.50 Sapphire development, or Napier's E.143."
Given the date of the Type 543 they must be a circa 1951 designs. I've not seen any other reference to the Sa.50 either, the Avon development might be what became RB.106.
It seems that these engines quickly died and were replaced by higher-rated developments of then-existing engines.
It's peculiar that they don't feature on any other requirements just after this period such as ER.134T or any of the interim transonic developments of the Hunter/Swift et al. drawn up circa 1951-52 and it's equally odd that Supermarine should choose all four unknown engines for its peculiar aircraft.