The issue of round pin unfused plugs often comes up during PAT Testing courses or as a telephone technical support question. This post gives more detail on this subject.
Last week, an apprentice at work showed me a plug on an extension lead that had overheated and was in a dangerous condition. He said that he had two 2 kW heaters plugged in. His question to me was "The current was around 17 Amps - why did the 13 Amp fuse not blow and protect the plug from overheating?"