Which to replace - the water heater or the 3-way switched plug adapter or something else
I was trying to figure out what "3-way switched plug adapter" meant until I Googled it and realized it's a UK idiom.  So you mean one of these? 



No. Just No.

Unplug that on-demand heater at once.  An on-demand heater takes far too much power to work with those adapters. It needs to be directly plugged into a listed receptacle.  Realistically, it should probably have its own circuit, and be hard-wired onto that circuit so no plug is involved at all.  (though UK does have nice beefy plugs). 

I think you'll find the heat is not from the plug proper, but from the 3-way adapter getting rather much too hot. 

Those 3-way adapters are intended for things like cell phone chargers or at worst, a television.  Big loads like a heater are right out.  If in doubt, look at the amps, watts or VA the device draws, if it takes more than about 2 amps or 500 watts/VA, it's too much for one of these.