A quick check of the element is easy enough to do.
Remove the lower vent cover and locate the exposed top elbows of the two heating elements (12V and 230V) as they enter the cylindrical jacket of the burner chimney.
Switch on the mains power to the fridge, check the green switch is illuminated and turn the thermostat to maximum. After about 10 minutes, if the element is working, the exposed part of the 230V element will be hot.
If it's not heating up then the element is faulty.
The next thing to check is whether the element is free to move - on older fridges they can be completely jammed in due to rust. Give it a wiggle to see if it's reasonably free.
Depending on how much room there is to access the back of the fridge it may be possible to replace the element without having to remove the fridge, however, the element's cable is connected to a junction box located behind the front green and red switches so the fridge will need to be pulled out enough for access.
From my experience it's much quicker to change the element with the fridge out.