Far too many people still believe that the purpose of a fuse is to save lives. Sadly, it is not, at least not directly. The purpose of a fuse is to save the circuit the fuse is in. The idea is that if fault conditions arise and the current in the circuit becomes too high, the fuse will fail, thereby preventing the wiring in the circuit from burning out instead. It is much cheaper to replace the fuse than it is to replace the entire circuit. The important point here is that a fuse will not necessarily prevent you from electrocution. It’s primary function is to save you money. It’s secondary function is to prevent your house from burning down.
To be sure of preventing electrocution you need your circuit to be protected with a residual current device (RCD) or a composite device which performs that function as well. RCDs detect whether the current flowing out to a circuit is matched by the current flowing back. If there is a difference, they shut off the current. This means that the moment a fault to earth occurs, the circuit is taken out of action. A fault to earth is where the current is flowing away from the intended circuit and into the earth, probably through your good self. This will save your life. In other words, an RCD will detect fault conditions which are the opposite of those which a fuse acts to prevent. RCDs shut current flow off very fast indeed; they work faster the more dangerous the fault is!
Of course, circuit burn outs are dangerous because they cause fires. There were 38,505 accidental fires in the statistical year 2010-11 (link is PDF download from government). 4006 of those were caused by the faults in the electrical supply and 4812 were caused by faulty appliances. I’ve done the maths for you: 23% of all accidental fires were caused by electrical faults. Therefore, a fuse might prevent you from burning to death. Replacing fuses which routinely burn out with a higher rate fuse will mean the circuit burns out instead. Incredibly many people opt for this daft solution instead of calling an electrician to inspect their circuits properly.