I would as well.

Probably meant to work from a 16A supply (or more).

You may find it'll work OK at lower power settings from a 13A supply, but go too far and you'll blow fuses or trip switches.

Look in the box,it comes with a nail for the plugtop on high settings.

Fuses don't blow at their rated current. There are charts for this. There is a lower and an upper curve, of time to blow vs current and the fuses are guaranteed to blow within the times stated at a particular current, somewhere between those two curves.

At, say, 10x overcurrent, it may be likely to blow in 0.4 seconds for instance, but it may do so with as little as 6x or as much as 12x (made up figures).

Even on the lower curve, a 13A BS1362 fuse will carry 21A for at least 2.8 hours and likely indefinitely.

The fuse may not blow but your wall socket will melt, been there.

Quite possibly. However, for intermittent use, it be unlikely to be a problem. Continuous use would be.

Depends what you're doing with it. IF you're running 200A continuous on some 5mm steel for 2m of weld, sure you'll see issues.

I have a Hitbox 200A mig/tig machine, runs absolutely fine over a 25m extension when welding 1mm steel because I'm not even close to the current limit.

You can generally push more than 13A through a 13A plug for a short while, but it will burn eventually even if the fuse doesn't trip. I've run an experimental hardware item on a 13A plug at 3.3kW, for the first 10 mins you'd never know, for the next 30 mins it was getting toasty. After that it was a controlled burn