Mathew Newton pretended :
Measuring the primary coil revealed it was open circuit.

Any ideas what could cause the transformer to fail? Do I dare rejoice that
I've fixed the boiler, only to find out soon (Christmas Day probably) that
there is an external component (e.g. fan?) that might be overloading the
transformer causing it to fail? Or could it just be age / poor design?

It was probably inadequate design or inadequate rating it was such a
common fault. You can actually buy, or could, identical replacement
transformers to avoid the cost of a new PCB. I repaired one that way,
but added extra ventilation around the transformer.

Another regular fault, is the fan and especially the wiring to to the
fan, which runs up the rear of the boiler. The heat from the boiler
melts the insulation.