Fuses & current ratings - are there fuses that blow "fast" close to their nominal rating?
I am looking for is the existance (or not) of fuses that do what most
people would expect them to do: blow in a short time as soon as the
current exceeds the current rating.

Fuses don't protect a kettle from damage should it suddenly develop the urge to take more current. They protect infrastructure i.e. the wiring of your home and, the wiring of your home can take excessive currents for a pretty long time before getting too hot and starting a fire. The fuse stops the house burning down and isn't capable of protecting your kettle, hi-fi or TV should it develop a fault that causes it to take more current.
If your kettle, hi-fi or TV takes more current (than it should do) then it's because it's about to fail.
Fuses don't protect electrical items, they protect infra-structure (including the &quot;usually-more-costly-to-repair&quot; product infrastructure).