There is no definitive answer. The remote possibility of damage is to the heat exchanger and only could occur if the burner was actually firing at the time it was switched off. Then it would depend if the water in the heat exchanger was hot enough to boil away causing a hot spot. Then it depends on if the hot spot is sufficient to cause deformation. Then by how much and is it enough to effect the unit?
Boilers shut down because of power failures and other reasons every day and there is no evidence to suppose the life span is always (or ever )caused.
Hi again. Thanks for your added time on this. I don't think it was firing or we would probably have been too alarmed to unplug. As I said, it was on the lowest boiler setting of '1' We have been awaiting the room stat. to be fitted and the installer- when asked how we switch it off- answered, 'unplug it'! I decided to use a timer for auto morning switch on but used the timer over ride switch to turn the boiler off at night. Is any possible damage accumulative, (maybe visible?) or a question of it still woks okay, it is okay? Thanks