I have an early Vibiemme Domobar Super electronic/automatic.

Today I removed the pipe between the boiler and the hot water wand to clear a scale blockage at the pipes connection with the boiler.

On reassembly as soon as I turn the rotary switch to position ll to turn on the water heater, it immediately blows the house fuse for the outlet the coffee machine is plugged into.

The heater element measures about 30.5 ohms which is about spot on for an 1800 watt 230V heater.

Resistance to ground from the two white wires connected to the heater is about 5 K ohms.

Resistance to ground from the two blue wires connected to the other side of the heater is
also about 5 k ohms

Both resistance value above measured with an automotive grade DC ohm meter.

If I remove the white wires from the heater, the fuse does not blow.

Does this indicate my heater likely has a short to ground when subject to 230V AC?

Yes, it's possible that the heating element have dispersion only once powered on, and by instrumental test does not show any clue.
But the machine was working regularly before you did the first repair?
Anyway, if can be useful i found a thread with the electric diagram, hoping it's your machine model.
Vibiemme Domobar Super - Electrical Diagram

Does it blow a fuse, a breaker or GFCI breaker/socket?

5kΩ maybe below the trip threshold for a 220V GFCI device

The heating element should be an open circuit to ground. It may be damaged and allowing electrical contact with the water.

I will need to confirm it whether is a RCD circuit breaker (which is what I think you refer to as GFCI circuit breaker?)

I think we call them RCDs in New Zealand.

"But the machine was working regularly before you did the first repair?"

Yes.

Many thanks for the link to the circuit diagram. I will check if it is the right one tomorrow.

I have a good diagram I made for the water snd steam flow throughout the machine, but didn't have a circuit diagram.

Thanks guys for your help the heater was indeed faulty. It was shorting (not a dead short) to the surface of the element.

I have replaced it and am no longer blowing fuses.

I now have the next problem to solve but will start a new thread for that.