Hi Adam , welcome to the Forum.
Could be a few things wrong . I'll a list the common problems I can think of.
1) Because of the heat involved ,connections often burn out to the elements. Check those. And at the local isolator switch. And inspect the flex .
2) The rod stat will often fail. See if it switches on and off. If tank is cold stat should be closed. It just pulls out of it's pocket and slide a new one in, of the same size.
3) Modern heaters have an additional overheat cut out which may operate .
4) The element in the water cylinder could be open circuit. Test for continuity.
5) The element may have split open or even a section dropped off . Insulation test to earth.
6) I always maintained that immersion heaters should be on an RCD as they will often carry on working even with just two open elements in the water .
7) I was also taught to ,if it still works but not very hot, to take a current reading and check it against the rating .
8) If its controlled by a time switch you need to check that too.
9) And finally is it as daft as the local isolator has been switched off. (It happens)
If its open circuit or down to earth ,it has to be replaced , I recommend you (a) isolate the supply (B) disconnect the heater ,noting how it was connected and © get a plumber to replace it.
Reason for this is , if you are not used to plumbing work its a disaster waiting to happen TBH.
You can easily split the cylinder when unscrewing the heater.
Often you can't fully shut the water off with manky old valves etc.
Often there are no drain offs on the system.
I've shut stop valves off in the past and they won't turn back on, then you find you are doing plumbing work without proper tools and experience.
