Sylvia Else wrote:
I have to phases of power supply to my house - so three power lines, two
phases plus neutral.

I suspect it is really "single phase" (think: center tapped
transformer) -- though in Oz they probably do things differently! :

I've on occasion wondered what would happen if we lost the neutral line.
It seems to me that we'd then have the voltage between the two phases
across two sets of appliances, one set attached to one phase, and the
other set attached to the other phase, with the two sets in series as a
result of their common connection to the neutral wire. Since the two
sets are unlikely to represent equal loads, the net result would be a
large overvoltage on one set of appliances.

"Large" is a relative term. Homes are typically wired to
try to distribute the loads roughly equally on the two
legs. And, REALLY BIG loads (e.g., air conditioner compressor)
tend to straddle *both*.

My electrician says it's not an issue, but I can't see why.

"Luck"? But, in theory, he is wrong.

The more significant issue is *how* you would lose neutral.
Here (US), your house is tied to *earth* at the main panel.
And, neutral is similarly tied to earth. So, you would
have to lose the neutral feed from the utility *and* the
earth at your house.

This has happened to two neighbors in the past 10 years,
though. I think in both cases it was caused by a cable
actually failing (corrosion). In one case, the folks
sharing his distribution transformer (typically four homes
to a transformer) lost power when the incoming power was
effectively *shorted* to ground, (I don't know what the
distribution transformers are fused at but it was enough
to set some adjacent utilities -- below grade -- on fire)