Today I sent a question on current rating and immersion element power to the Backer Electric Company Limited. They confirmed as Johntheo mentioned above that their Backer stats rated 20A can indeed directly control a 4kW IH element. Whether other makes of stat can is another matter.
brixtonia: 1. The question about the rcd is to see whether the 4kW element albeit a new one is leaking current to earth - unlikely if new but maybe this is a cause of overcurrent.
2. I'd love to have some pictures of the installation to study. Are push on spade terminals used for any of the connections? Are they bare metal or shrouded types?
3. What is the supply voltage?
4. Does the installation have a large solar pv system feeding into the grid which might be elevating the local mains voltage? Are the large solar pv arrays nearby which might be raising the supply voltage?
5. Forgive me - is the wiring definitely 2.5mm2 csa?
6. The 16A safety stat is under-rated.
7. What temp do you have the control stat set at?
8. What is the length of the link between the control and safety stats?
Probably enough for now. But some images of the point of failure on the control stat external terminals would be useful to see.