Note that the 3.7kW element can only provide all that to a single vessel if it covers the entire area of the element.

The resistive element submerged in the water dumps very nearly 100% of energy into the water. The stove heating the kettle has many more sources of loss, but mostly that it first heats a piece of metal, which is not fully submerged in water.

What is the power of your kettle?

Install an A/C socket in your kitchen. Then buy a British 240 volt 3 kilowatt kettle from eBay and wire on a US A/C plug (NEMA 6-15) - hooking the brown and blue wires from the kettle to the two line pins, and the green/yellow wire to ground.

This would be both code legal, safe and functional.

It would also be possible to use a clothes dryer socket (NEMA 14-30), but you should install a smaller than usual breaker for the circuit (15 amps), since the british kettle normally has a 13 amp fuse in it's plug, but a NEMA plug does not contain that.

Pretty much. My office building was formerly a woodworking shop and has wiring for 220V. Long ago I bought a laser printer on eBay. The seller omitted to mention it was a 220/240V model (probably why it was cheap). Laser printers unlike most appliances are not dual voltage because the fuser is run directly off the ac supply line. So I wired in a 6-20 outlet and changed the plug. Worked fine for many years. I also have a table saw running from a 6-20 outlet. There is a 6-15 NEMA type that presumably would provide a UK compatible supply. I think the problem might be how to provide in-wall cabling that's to code for 220V. In my case I already had conduit with THHN wire.

Not necessarily to code, consult your electrical engineer and lawyer before doing your own wiring, etc.

I use a Panasonic flatbed microwave to heat precisely the volume of water I want by filling the tea cup(s) I want.

Two minutes on high (1100 watt microwave output from, IIRC 1800 watt input) per cup. So usually two minutes for the one cup of I intend to drink.

Every electric kettle I’ve ever owned has a minimum volume of at least two cups. Who bother heating two cups if I’m only going to drink one at a time.

Tasmania (AU), 240v / 100amp supply to residential is standard.

It does in theory. There are a few taps in the UK that are marketed as being able to produce essentially boiling water (which is what our typical tea bags require). Though we tend not to put quite so much money into our kitchens.

And we would wear those things out, I swear! :-)

I think Americans think British people drink tea out of poshness, when it is the opposite. Most of us also like a posh tea now and then, some of us drink expensive leaf teas... but the majority of what we drink is optimised for fast brewing off boiling water: tea that goes black in the mug in thirty seconds in boiling water.

There is a concept here of "builders tea" -- the kind of thing a builder drinks -- which is sort of the functional equivalent of cheap electric coffee-pot coffee. That is, it's the kind you know isn't the best, but you will still drink it, and that cuts across all class lines. [0]

There is a parallel thing: the "tea urn", which is like an enormous samovar with a lever -- that you still will see in industrial canteens and at church coffee mornings and at gatherings that aren't at cafés or restaurants. Those things actually need a different kind of tea, which brews more slowly and at slightly lower temperatures. The end result is a bit like builders tea. But we wouldn't bother with them at home.

[0] We do absolutely drink coffee at home, but aside from appalling instant coffee we tend to skip over the coffee-pot coffee in the UK, to slightly more expensive ways of making coffee or to dreadful Nespresso machines. You'll see more of those or Bialetti mokas here; old style electric coffee pot percolators are now rather unusual. But Alan Adler's Aeropress particularly caught on here among coffee nerds, because that is really compatible with electric kettle life.