In reply to Howard J:
Don't think it'll damage either the kettle or the hob - it's just that some stainless ones won't work.
Stainless steel is complicated - some variations are magnetic and some aren't. Testing with a magnet is reliable but that's only useful if you're buying it in person.
We use a Le Creuset kettle on both our gas and induction hobs - looks like they can be had for £40-ish used, and they look good and last forever.
I've not measured it accurately, but I would imagine that using a kettle on induction will be more or less exactly the same efficiency as a regular plug-in one. For both of them the major loss is conduction through the walls and that's going to be broadly similar. Gas will be much less efficient (lots of the heat of the gas never gets into the kettle) but cheaper overall (as gas is 1/3 the price of electricity).
Oh - and yes, the inductor can be quicker than regular electric. A normal kettle is limited by the 13A connection (so a theoretical maximum of about 3000W, but in practice usually around 2500W). If you have a dedicated supply to your inductor that can be higher - mine puts out 3700W, so it's about 2/3 the time to boil.
Post edited at 10:13