I found the marriage entry for William Greentree and Annie Agatha Gray and unfortunately it doesn't give marital status to indicate whether he could be a widower. I have found the death cert of Annie, who died first, the information supplied by their son Geoffrey. William died as the result of brain injuries accidentally received by a fall in the Hospital Ward, so the informant was the coroner, the children's names are basically the same, except William has a note of one male deceased which is not on Annie's.
I think the way to go is to get Laurie (George Lorimer) birth cert, which should give me at least where his father was born, his age and whether he had older children.