Thankyou Osprey,
That is a start! Thanks for helping me find the image. You are right about the Edmund. Not definitive at all. We only know of one son, Thomas (no middle name

) He came to Australia with them, any other children were presumably fostered with either Mary or William's family.
...However, Thomas sparked off a dynasty. Some middle names that may be significant:
Trefusis (this name is very strong in the family but believed to be a very early Bawden connection eg "Mr Bawden was made a freed man of the Castle Trefusis in 1450")
Warne
Penberthy
Dobie
Connor (unusual for a female middle name?)
These names may be a place to start?
With William listed as a sojourner, could we expect that his home parish was a long way away? Or could he have been from just up the road so to speak?
I can see that a Bawden married a Warne in Perranuthnoe in 1836 (only a few miles away) wrong gender (and timeframe) to be grandparents, but maybe friends of the family? Perranuthnoe is close by. What do you think? I cant see anything for any of the other names I have mentioned.