A 3kW immersion heater would draw ~13A from a 230V supply, so just within the rating for a 13A socket, and well within the rating for 2.5mm^2 twin and earth so, in theory, it is fine. Not keen on the idea of a 4-way extension block being used, even though it is probably rated for 13A. Not sure what the current regulations state. Running the solar thermal setup from the same "four blocker" would take the current passing through the mains socket, plug and cable to over 13A.

If there's no hot water during the present weather conditions, then that seems odd, if there is a solar thermal setup involved. Is the solar thermal system working as it should? Do the sensors give sensible readings and, if so, does the solar thermal pump come on as expected, when there is a suitably large temperature differential, and does the pump appear to move the thermal transfer fluid correctly?

Solar is the old set up of one tank heated by solar which feeds the main hw tank, leccy pull will be minimal, and yes it all seems to be working okay.