A bit of luck and a calculated guess helped solve this search. The WA RSL sent me the WWII group of five medals awarded to WX9592 Thomas Anglesey but I kept running in to dead ends. There are only four soldiers with this surname on the WWII nominal roll so I followed a hunch that some might be related.
To my surprise I found that Thomas' service record had been digitised and was on the National Archives web site, here. This gave me his next of kin name and address. I noticed that the records to the other soldiers with the same surname were also digitised so I went through them and worked out that WX4158 David James Anglesey was Thomas' brother. From all this I was pretty sure that Thomas never married. However, I knew that David did marry.
I found David's funeral notice at this link which gave me his son's name, being Sam. I then took a punt based on names and geographic locations and ended up speaking to Sam's son. So the person I found is Thomas' great nephew.
The returned medal tally is now 933.