I watched my daughter boil the electric kettle, and pour the water into the pan, and asked her why, she said it was faster, and I replied I don't think so that ring is rated 5.5 kW and the kettle is 2.8 kW.
So she did the demo, filled kettle to mark, poured it into a pan, filled again to mark, turned of gas, and turned on the kettle, and there was a very marked difference in the time, lid was on the pan, but it took some thing like twice as long, so if twice and long to boil and twice as much power being used that is ¼ the efficiency of gas.
So there is not real gain using gas to boil the kettle, in fact if to factor in how much hotter it makes the kitchen, and the fact you need a cooker hood to remove combustion gases, then it is likely more expensive to use gas.
But maybe due to using a hob rather than kettle, so when I got home, did the same test, and the 3 kW induction hob boiler the water same time as the 2.8 kW kettle.