So when you say, "I'm going to put the kettle on," you're referring to putting the kettle on the counter, not the stove? Or do Brits not use that expression for using a kettle.
Erm... not quite in the same sense IMHO, we're still putting the kettle on to boil. When I flick the switch, the kettle is 'on'. It's even in the 'on' position :)
I'm not sure the etymology of "put the kettle on" has been strictly about a stove-top for a very long time. To me it's a method-independent phrase, and a reference to setting the kettle to boil, not its physical placement.
When cast-iron stoves were common and possibly the primary source of heat for many homes, I am pretty sure that for most of the cold parts of the year, they would be fired-up and kept hot most of the day and night for warmth.
So - it wasn't a big production to boil water, you would just put it on the already hot stove.
(And also - I did not know this until recently but kettle can mean just a large cauldron/pot - although typically it would also have a wire handle and a lip/spout for easy pouring. Hmmm they were also used to hang above campfires, so my stove theory might go even further back...)
Ah, that makes sense! I guess I was assuming that "on" was in reference to it's placement _on_ the stove. But turning the circuit _on_ makes sense too.
Kettles on stoves are weird to us.