The prime purpose of the fuse in the plug is to protect the cable attached to the appliance. For example, where the cable rating is 6 Amp, we need to make sure that the fuse fitted is either 3 Amp ar 5 Amp. Clearly a 13 Amp fuse is not going to protect this cable.
Having said this, my colleagues and I have come across a number of appliances where the fuse in the plug is 13 Amp, but the cable is only rated at 10 Amp or sometimes only 6 Amp. The marking on the cable on a travel kettle that was purchased recently had 3 x 0.75 marked on it, indicating that it had 3 conductors, each of 6 Amp current carrying capacity. This was a newly purchased appliance and not one where the cable had been changed by someone.
This has puzzled me as I wasn't sure how such an appliance could have meet the Low Voltage Directive.
In Edition 4, Note 2 regarding Table 6.1 says "Where a manufacturers' flex is less than 2 m in length, has a csa of 0.75 mm2 and is fitted with a non-rewirable plug, it may be rated at 10A and be fused to 13A, in accordance with BS 1363 Table 2 Note C.
In summary, this is a very useful bit of information that helped to clear a mystery for me. If I find any more useful practical information like this in Edition 4 of the COP, I will post this on this blog.