We have a HNQ question on that right now over on diy.stackexchange.
That problem is a little different since that person gets 2 phases (hot-neutral-hot), and most UK homes get only one (hot-neutral). But your situation is absolutely identical to my own situation last year -- we're an outlier for the US, but our units get single phase just like you (of course, it's 120V), but our estate is served by split-phase (2 phases of 120V each). Half the flats are one one phase, the other half are on the other phase.
Split phase power is a line - 240V "long" with neutral in the middle. So it's very easy to see the behavior of a lost neutral; each phase is higher or lower than 120V, but the dead giveaway is, they add up to 240V.
We lost our neutral wire. So our flat was (tending to) see voltages go down to 80 volts, but simultaneously, half our neighbors were seeing 160 volts. So they blew a bunch of appliances. I figured this out because my storeroom is on the other "leg" so I was able to run over there and measure 145V. (uh oh!) Our voltage was lower because our "team" was in a tug of war: by pulling more current, we were pulling neutral closer to us, lowering our voltage and raising theirs.
It's your exact same situation with the "tug-of-war", except 3 teams instead of 2, and your playfield is a triangle. You occupy one corner of the triangle. The triangle is 416 volts on a side, with 240V to the dead center of the triangle. That dead center - neutral - has become un-pegged. If your team uses more current, you are pulling neutral toward your corner, raising voltage for the other teams. The highest possible voltage is 416V.
If the transformer is wired correctly, current will also try to return through your earthing system (the grounding electrode system in North American parlance) which will tend to pull neutral back toward the middle. That's how the linked question had less extreme voltage shifts than you might have expected, and why there was current moving on the grounding electrode. If your transformer's connection between its neutral and its earthing system is broken, that won't apply, and voltage shifts can run the full gamut clear up to 415V.
In the UK and the five continents which are not North America, most consumer power is wired so each flat gets neutral plus one of the three phases of power.