As we have no working boiler only an electric shower and while I wait
to see if the boiler can be fixed or needs replacing, I notice we have
immersion heater in the hot water tank but it's never been connected.

I assume this is a 3kW heater - does it have to have its own circuit by
regulation or can it be powered from a nearby circuit already powering
the heater controls. This would only be temporary and be a backup to
when the boiler is fixed.