If you apply 240V to a circuit designed for 6V, the fuse will probably blow because the current in the circuit would be multiplied by 40 (240V/6V), thus the fuse would dissipate 40

Fuse Markings Explained - Swe-Check Fuse Markings Explained - Swe-Check

If the fuse's resistance increases due to heat, and the load's resistance remains unchanged, the voltage across the fuse will also increase slightly, heating the fuse further and thus accelerating the blowing process. It is the current that a fuse is able to interrupt without being destroyed or causing an electric arc with unacceptable duration.Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. If you don’t see what you are looking for just let us know and we will locate these fuses for you elsewhere. Over that and it will blow, the greater the overcurrent the quicker it blows, depending on slow- or quick-blow design, etc. If 6V DC was applied to this example fuse, 240 watts in this condition would be 40 A when the fuse would 'blow'. When you drop an egg the chicken and the egg arrive at the impact point at close enough to the same time.

Littelfuse 217 - Littelfuse

I think that most people ignore the voltage because they assume that it remains fairly constant, which is true in the vast majority of the cases. However you cannot use a low voltage fuse in high voltage applications : it will still blow at (strictly, slightly above) its rated current, but may sustain an arc that a HV fuse would extinguish.