If the appliance has 0.5 sq mm cable, the UK plug should (maybe "must" because of the wording in the Plugs and Sockets Regulations) be fitted with a 3A fuse, or 5A if high inrush.
If the appliance has 0.75 sq mm cable or above, the UK plug should be fitted with a 13 A fuse.
Before you get to selecting fuse size, you have already selected the cable based on the following (in Table 2 of BS1363-1 as mandated by the Plugs and Sockets Regulations):
Appliance Rating Cable Size
<=3A 0.5 sq mm or greater
<=6A 0.75 sq mm or greater
<=10A 1.0 sq mm or greater (0.75 is allowed if <2m cord)
<=13A 1.25 sq mm or greater
(noting the max size that will fit in a UK plug is 1.5 sq mm).
These rating figures are determined by the temperature the cable may reach in operation.
The fuse size is determined by using a "non-adiabatic" method, looking at whether the cable will overheat in a direct short-circuit.
The only limits on flex length (apart from 0.75 sq mm with a 10 A appliance) are relating to volt-drop (or Class I touch voltage), and not short-circuits.
So, how does this relate to your tin opener?
Assume current < 3A, manufacturer must choose flex not less than 0.5 sq mm (from Table 2 of BS1363-1). So he chooses 0.75 sq mm. Then needs to size fuse, and again refers to Table 2 of BS1363-1 which says that 0.75 needs 13 A fuse.
Manufacturer then ensures (with the aid of the appliance safety standard - in this case the appropriate parts of BS EN60335, I'd guess) that the tin opener will not cause fire or shock or burns in a fault with the selected fuse let-through, and presto - design complete.
If the appliance has 0.75 sq mm cable or above, the UK plug should be fitted with a 13 A fuse.
Before you get to selecting fuse size, you have already selected the cable based on the following (in Table 2 of BS1363-1 as mandated by the Plugs and Sockets Regulations):
Appliance Rating Cable Size
<=3A 0.5 sq mm or greater
<=6A 0.75 sq mm or greater
<=10A 1.0 sq mm or greater (0.75 is allowed if <2m cord)
<=13A 1.25 sq mm or greater
(noting the max size that will fit in a UK plug is 1.5 sq mm).
These rating figures are determined by the temperature the cable may reach in operation.
The fuse size is determined by using a "non-adiabatic" method, looking at whether the cable will overheat in a direct short-circuit.
The only limits on flex length (apart from 0.75 sq mm with a 10 A appliance) are relating to volt-drop (or Class I touch voltage), and not short-circuits.
So, how does this relate to your tin opener?
Assume current < 3A, manufacturer must choose flex not less than 0.5 sq mm (from Table 2 of BS1363-1). So he chooses 0.75 sq mm. Then needs to size fuse, and again refers to Table 2 of BS1363-1 which says that 0.75 needs 13 A fuse.
Manufacturer then ensures (with the aid of the appliance safety standard - in this case the appropriate parts of BS EN60335, I'd guess) that the tin opener will not cause fire or shock or burns in a fault with the selected fuse let-through, and presto - design complete.