It was John W (William) Williams. He did marry Annie Brennan. The other man in the hat is his brother, Rinky (maybe Arthur as he looks younger than John). I asked my mother but she could only remember him being referred to as 'Rinky'. John and Annie had three boys and a daughter. One of their sons was my grandfather, Clement Arthur (Dick) Williams. When he married he built a house behind them at Gilleston Heights (near Maitland). They all worked in the mines around the Hunter Valley region. He died in 1960 at age 70. My mother grew up next door to them and has very fond memories of him and Annie from her childhood.
Cheers JMCDD