I rather doubt that an inrush current would last long enough to blow a BS 1362 (that had adequate rating for the running current), even if that inrush current were appreciably more than the fuse's rating.The C13 IEC is rated at 10A. If the cable was 0.75mm I would put a 5A fuse in the plug, if the cable was 1.00mm I would put a 10A in if I had one, or a 5A.
It’s very unlikely any equipment that has a C13 fitted to it would draw anywhere near 5A, the only issue would be if the equipment had a high inrush current which could blow a lower amperage fuse, such as a vacuum cleaner.