Ok so here's a potentially interesting update following your suggestions
@dlockers and
@b0rn2sk8 especially.
I had another look at the Zappi charger. Turns out as you say, it's somehow connected to the mains and it displays the current power draw of the property, and seems to mirror my IHD pretty accurately. Which means I don't need to isolate circuits inside the house, I can do it from the mains boards in the basement next to where my smart meter is.
These are the mains circuit breakers that supply everything in the property. They're right next to my smart meter. I had a look at the meter, it shows my usage in kWh but that would mean having to turn everything off and wait an hour to see if it goes up by 1kW which isn't practical.
So I did the next best thing, I found the small breaker that supplies the Zappi and the Zappi only, left that on, and turned every other breaker off from the mains for the entire property.
Lo and Behold, the Zappi displayed 0.0kW for the first time.
Turning breakers on one at a time, starting with the far left on the picture above, the Zappi went to 0.4kW. The second one then turned most things in the house back on it seems, as Zappi went back to 1.1kW which is my standard baseline where it then remained.
So I guess that rules out a fault with the smart meter since it went to 0.0kW? And it means there's something dodgy on the property itself?