A bit of the existing wiring and number of solder connections on the unit are questionable and will require attention as well there is no mains power switch incorporated on any of the potentiometers and I may also look at addressing this as I do have a collection of switches and other switched potentiometers, the mains and fuse situation as previously pointed out without question needs to be tidied up but I am not sure if the chassis is meant to be earthed, our existing valve radio does have continuity between the mains earth plug and the metal chassis depending on where you probe, brass fixing screws seemed to be the best place.
They generally are Muttley unlike old TV sets that have a live chassis. .
Live chassis BW valve TV sets are very,very rare in Oz---They almost all used a power transformer.
The only exceptions I can remember offhand were a few early "portables" from Admiral,& perhaps Stromberg-Carlson,or Healing.
Maybe the situation in NZ was different.
Some country towns still had DC Mains in the '50s,so some AC/DC mantel radios were built for that market (pretty much as "special orders").
Apart from those few,the "all-American Five" style of AM radio & its Brit & Euro equivalents never took off in Australia,as transformers were cheaper to make in this country than the extra insulation needed with transformerless construction,to say nothing of series string valves.
AWV & others turned out enormous quantities of normal 6v & 12v heater valves,& very few other types.
In any case,transformerless designs were very much frowned upon by Electrical Authorities.