Hi Rod
Welcome to RootsChat

I got the sense that there was likely more to found in determining the eldest son, William's, origin.
I did search for a birth under Cross but nothing jumping out for him in London. Have you seen that research document I mentioned for him on the Ancestry tree (could well be your tree!)? Looks like the puzzle has been there all along. If you haven't seen it, it is certainly worth looking through as it shows all the things that have been checked to try to find his birth (similar problem finding George Snr's origins isn't there?).
I did search birth in Ireland for William but again nothing coming up.
Rootchatters love puzzles

So, come back soon when you get home to Australia.
Have a great holiday here

Monica