How have my neighbours’ appliances been damaged?
A broken neutral can cause serious over-voltages on an electricity supply.

UK supplies are usually three-phase and neutral, with approximately 415V between phases, and 240V between any one phase and neutral.  The secondary of the substation is "star" wound, with the neutral being the common point.  Most UK houses are supplied from one of the phases, plus the neutral.

If the neutral becomes disconnected at the transformer, then there is nothing to keep the phase-neutral voltage at 240V.  Instead, it can drift wildly, depending on what appliances are plugged in in each house.  The worst case is that one house may see the phase-neutral voltage collapsing to near 0V, while another sees anything up to 415V.

The houses are effectively connected in series between the phases, so the voltage varies with the resistances of whichever appliances are plugged in at the time.