Immersion Heater Suddenly Not Working?

If the light on the switch is on then yes your supply is good .Turn off the supply remove the element cover and look to see if there is an over heat button also inspect the connections to see if there is any evidence of fault (it will be obvious) the over heat button will be on the thermostat or on it's own in line with the feed to the thermostat when pressed it should click .don't forget to refit the cover before switching the supply back on.