BS 1363 13A Socket Continuous Max Load

Having said that how long does it take for a 14 amp load to blow a 13 amp fuse?

Well, more or less ‘forever’.

Actually a typical 13A fuse will carry 20A for long enough to get the pins hot enough to give you a nasty burn  and to weaken the springs in the holder and the socket. (10^3 seconds is about 15-20mins, and 10^4 seconds is something more like 3 hours… ).  There is no safety value in 13A fuses on a  circuit covered by a16A MCB, and not that much point in 13A fuses supplied by 20A MCBs, as the range of  fault cases where the 13A lets go first is pretty narrow.

The two curves represent  the 'all fire' and the 'never fire' conditions - real fuses have a considerable spread due to wire tolerances and variation in alloy mixture and so forth, and then on top of that the environment, i.e. how well the fuse caps are cooled, has an effect at on the exact boundary shape - if the fuse is running hot, then it  takes less of an overload (time or duration) to melt it.
Actually all fuses and breakers are like this really, just for BS 7671 we are more interested in the 'all fire' condition, and concentrate on that side of the curve, and often assume that the other limit might as well be a single value, the rating on the fuse body, which it isn't.

The unfused adapators are a bit of a throwback - remember these ? ( flameport website) My grand parents place had loads, on circuits protected by 15/20 amp fusewire.

Having said that how long does it take for a 14 amp load to blow a 13 amp fuse?

Well, more or less ‘forever’.

Actually a typical 13A fuse will carry 20A for long enough to get the pins hot enough to give you a nasty burn  and to weaken the springs in the holder and the socket. (10^3 seconds is about 15-20mins, and 10^4 seconds is something more like 3 hours… ).  There is no safety value in 13A fuses on a  circuit covered by a16A MCB, and not that much point in 13A fuses supplied by 20A MCBs, as the range of  fault cases where the 13A lets go first is pretty narrow.

The two curves represent  the 'all fire' and the 'never fire' conditions - real fuses have a considerable spread due to wire tolerances and variation in alloy mixture and so forth, and then on top of that the environment, i.e. how well the fuse caps are cooled, has an effect at on the exact boundary shape - if the fuse is running hot, then it  takes less of an overload (time or duration) to melt it.
Actually all fuses and breakers are like this really, just for BS 7671 we are more interested in the 'all fire' condition, and concentrate on that side of the curve, and often assume that the other limit might as well be a single value, the rating on the fuse body, which it isn't.

The unfused adapators are a bit of a throwback - remember these ? ( flameport website) My grand parents place had loads, on circuits protected by 15/20 amp fusewire.