Historically there is no set version of a full english. What you describe is just your version. It will be, entirely, a social construct. This is why the full english varies so much, its different traditions in different areas and families being passed down, giving everyone a different vision of what it is.

Its similar to how everyone has their own christmas traditions, or how fish and chips in the north tend to be more traditionally served with gravy mushy peas and bread+butter. Whereas in the south, typically, they are sold with just ketchup or mayonnaise. But again, not exclusively. They only requirement is a fash and some chips. Everything else is just a variation of that but still counts.

This is why i belive that there only needs to be a few core ingredients for a full english to qualify as a full english. After that its all tradition and preference.

Its a fair point and i see where you are coming from but would it not also be fair to say a that a "fry up" is a colloquialism meaning full english? I would ask, where does a fry up cease to be a fry up? Whats the minimum requirements? Is eggs on toast a fry up? Eggs and sausage and beans? Sausages and bacon and toast? Or all of the above?

Or does fry up refer to how its cooked, in that it all goes in the pan? I tend to grill my bacon and sausages, fry my eggs and mushrooms, toaster my toast, microwave my beans. Is that not longer a fry up because its not all in the frying pan?

As to your point about the ingredients being common in a few places like Australia and America. Is it not fair to say that they adopted the meal and that explains the commonality? Like in england a curry is a practically a national dish, but its adopted from indian cuisine. We make it slightly differently to its country of origin but at its core the ingredients required to call it a curry are not uncommon anywhere in the world.