Does anyone have experience of what happens when there is an unscheduled power cut in the area and they have a 3-phase connection? Do all three phases normally go down? Does the DNO shut off all three phases if they detect one is broken? Alternatively, does it happen that only one phase gets knocked out? Anecdotally, it feels like power goes off to the whole road and, since the DNO share houses across the three phases, that suggest all three phases go down during a power cut.

If power cuts often only affect a single phase, then the following product could be of interest. Otherwise, it seems a tad pointless in the UK.

GEYA Electrical

GPS6-N4VA2 4P Automatic Changeover Switch - GEYA Electric...

The GPS6-N4VA2 4P Automatic Changeover Switch (ATS/ACS) is a high-performance 3-in 1-out phase selector designed to ensure uninterrupted power supply.

I believe that generally all phases will go. The utility wants to balance the current on all three phases so if things get unbalanced to a significant degree it's likely to cause the transformer protection circuitry to trip all phases.

If you are running three phase equipment then detecting a missing phase is important as missing phases can happen due to relatively local wiring issues (not main grid stuff). But there is likely nothing in a home that is worried about this.

That is an interesting device, though if you have critical equipment that justifies something like this you likely have a UPS and can use a normal transfer switch (which I would choose in preference due to being able to choose a tried and trusted brand vs relatively new Chinese one).

We don't have three-phase power, but the houses in our cul-de-sac are on different phases. We've been here for 28 years, and when we do lose power, it's common for some houses to lose power whilst others are still live, so I would guess if I had an upgrade to three-phase, I wouldn't lose all phases depending on the circumstances of the fault. We do have occasions where everyone loses power, but that's quite rare and means a substantial issue in the area rather than something more localised.

At the end of the day, I would guess whether you'll lose all phases or not would really depend on why there is a fault.