A 13 amp fuse is just that, to protect a cable up to that rating.
You would be bloody mad to think you could somehow "up-grade cable" and exceed 13 amp loading just because these fuses are rated "Super fuse"!!

One would think so, but on my degree course a large part of one module was taken up with "fuses" !! In the lab we could consistently get a 13 amp fuse to take up to 25 amps without blowing, especially if the current was increased slowly, pulsed and cooling applied to the "fuse" !! So called "fast blow" fuses would regularly fail at around 11 amps !
Remember .. a fuse "blowing" is simply the wire overheating and melting ... the quality of the wire, the rate of heat dissapation v the rate of heat application, and even the style, quality and position of the fuse holder all make a big difference to the actual thermodynamics of the item !!
The other thing folks forget is a 13 amp fuse is designed to CARRY 13 amps .. not fail at 13 amps .. it should fail at 13+ a tad .. but they all have "leeway" depending on how well they are made.
If fuses were as good as some folk think they are then electrical items would never catch fire ... but they do, with regular, and dangerous, monotony