There may not be a "rule" or "regulation" but it is (sort of) obvious by logic and design.
That's why the OPDs are there - to prevent damage to the cable and fire.
That is how circuits are designed. Design current of load > next size up OPD > next size up cable.
Nobody would fit a 250mA fuse for a single table lamp.
The 13A fuse and 13A plug were introduced because of the 32A ring circuit without which the flex would have had to have been the equivalent of 6mm² because of BS3036 30A fuses.
Without them (13A devices) Britain would today presumably have the same 16A radials as Europe with 16A plugs without plug fuses.
Had metric cable decided to be, what?, 3mm² then, with the introduction of MCBs, the ring could simply have been done away with, with no alteration apart from disconnecting one piece of cable, and left Britain with 3mm² radials with 32A MCBs.
While it may be said that the 13A fuse, and 16A circuit OPDs, might protect the appliances (from what?), there can be no reason to fit lower rated fuses unless lower rated cable is used (433 aside).
That being said does any appliance actually require lower protection from the fixed installation?
There cannot be any, can there? Europe would not be able to use them if they did exist.
Those that do need lower protection have internal fusing, presumably (obviously?) because the fixed installation does not have to cater for it.