Quick answer
An immersion heater can become a noticeable cost if it runs longer than needed or is left on without a sensible timer pattern. Short controlled heating windows are usually the key.
Running cost guide
Immersion heater running cost
Immersion heaters are simple to understand electrically because they draw a lot of power for a set time. The main cost driver is how long the element is actually heating for.
Related route
Use the general appliance running cost calculator for a quick timer-based estimate if you know the wattage and hours used.