UPDATE - FULLY REPAIRED!So following james_s' comments, I decided to drill the welds and have a look inside the unit. Good god, so much shielding! Fortunately what wasn't welded had some fairly brittle epoxy holding it all together so after drilling 6 or so welds I was down to the core.
Inside the core, was two steel wires going into the core. One of these was soldered to the center tap, the other was attached to nothing... the winding just wasn't there! Over the other side was the wire for the other end of the winding, but this wasn't where the wire had been attached to - it was on the other side. So presumably this was a single unit for 120/240v configurations with the wires attached to center/outer or outer/outer taps depending on market?
So I stripped back the other end of the winding and fed in 240v... and got ~20v on the output!
I soldered it all back together, put a thick layer of JB Weld over it all and left it overnight, then wrapped all the shielding back around it with a couple of fat cable ties in lieu of the welds. No other problems apparent now we've got power either (almost disappointed - was hoping for a bit more of a challenge lol)
Feels like I repaired something that probably isn't ever supposed to be repaired, but happy with the result! Thanks to all who offered advice
Will post up pics if anyone's interested.