I'm surprised to see such misconceptions about fuses flying about in professional electrical circles!! Fuses are NOT overload devices - they are Overcurrent devices - they provide short circuit protection ONLY. A BS1362 'plug top' cartridge fuse will not protect the equipment connected, nor provide overload protection ( well, not below about 1.6 times the fuse rating). The rating is the safe current the fuse will carry forever. Above that things start to get warm, then hot. A 13A fuse will carry 30A for 6 minutes or so, 50A for 0.1 to 20 secs, and 100A for 10 to 20 msecs. I believe it would take 1.6X rated, ie 20.8 A indefinitely, though things would get rather hot before too long! So, either fit some proper overload device, or a good smoke detector!