Hi Paul, make sure your cable from immersion to the plug socket is the right armoured strength for a 3kw element!!
Others will be on who can remember the specifics (Peavey Wolfgang
etc).
I had 3kw off my mains with normal sockets (it had circuit breakers) but downgraded to 2kw as I couldn't go to the 16amp set-up, and my plug got frighteningly hot. All OK now.
You'll be OK with the right 16amp set though.