It depends what you define as an "appliance".
For example, connecting an electric hob or fan oven to a 30A supply is somthing that's best left for a competent person. That's true here in the UK if what you're doing is covered by part P.
https://www.gov.uk/government/publicati ... document-p
(Which is excellent bed-time reading.)
I have a friend who found a 30A cable buried in the wall of his kitchen (they cooked on gas). It was a wonder he didn't die when he cut that one with a pair of pliers only to discover it was still live. The electricity board were quite shocked (excuse the pun) when they were called to come and make things safe before replacing the 100A company fuse.
There's nothing to stop me building electronics/electrical equipment designed to be connected to a 13A square pin plug. There isn't even a requirement for portable appliance testing of things for my domestic use (although my eldest can do that for me if required since he's a sparky).