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The one I know about was Stephen Penberthy, who died in 1880 in Pinkertons Plains, South Australia. I'm sure there are distant cousins in other parts of Australia. I don't know of any Bawdens who went to Australia, but there are Bawdens in that particular Penberthy line. Stephen's great grandfather was Joseph Bawden born 1768 in Phillack, married to Ann Bawden. Joseph died 1835 in Lethlean.
I'll have to go and read the thread you mentioned.

Thanks very much for the info.
Yes, it certainly appears that Francis White was a tenant. He is called a sheep farmer. He or his family originally leased from Sir John Owen, according to the article "Paterchurch: A Mystery Solved" by M.N.E. Tiffany  in the Journal of the Pembrokeshire Historical Society Vol 5 1992-1993 by M.N. E Tiffany (Welsh Journals Online). By 1820 White was a tenant of the Board of Ordnance, according to the same article.
Another online article says that the White family were tenants of Paterchurch Farm from 1776 to 1812 (this article is from "Gazeteer" material to be found on Cenquest and taken from work originally done  by Basil Hughes. An interesting online article on the  Pembroke  Dock Community Web Project: The History of Pembroke Dock website states that Mr. White accepted over 4000 pounds in 1813 from the admiral in regards to use of the land. The original article was written by Ron W Watts.
I think the Francis White who married Esther Prout in 1760 must have been born about 1730. He can't possibly be the Francis White who was born in the late 1600s. I don't think the Francis who married Esther married a second time, for Esther clearly lived a long time. Francis and Esther are parents of Margaret. I am looking for more information on Francis and Esther.

Thanks very much. This is a lot of information and should be helpful. I do have from the very comprehensive book about the people of Pembroke Dock (I did not write down the title of it when I borrowed it but it was something like Pembroke People)  that William Streets is from Bristol, and married Mary Davies, daughter of Hugh Davies.. Hugh was also not of the area. Son Joseph married Margaret White. The same book shows that Francis White, possibly son of Francis White of Studdock, (the older one born 1698), may have married Hester Prout 1760.  Apparently the latter Francis White , OR the former, as a widower,  if I understand the text correctly, is parent of Margaret White, who married Joseph Streets of the Dockyard. in 1808 (Nicholas Roch officiating). Francis and Esther White were witnesses at the marriage.

I think it is very confusing that one generation got lost, but I will look over all the material you provided and see what I can figure out. Thanks very much.

I believe I have found the story and people I was looking for.
Stephen Penberthy, of the correct age to be the brother in question, died in a construction accident in Quorn in 1880. I don't know how the Sydney bridge got into it.
I found the story in an online newspaper.