Is it safe to not have a safety cutoff on an immersion heater?
Hot water coming out of your taps is a serious safety issue as an unsuspecting person could scald themselves. It could cause damage, so an emphatic yes, this is an issue that needs resolution. 

There are 2 problems I see here:


No Thermostat: every heater should have a thermostat, or a control of some kind to prevent overheating. It's not just for safety, overheating reduces the life of the heater
Hot water getting into the cold supply. This shouldn't happen, an overheat should lead to some sort of pressure relief which dumps the hot water safely


This system is unsafe and I'd be surprised if it was up to code. Your landlord should fix it.