The first thing I'm going to ask is, "Is the cable large enough to take this size of heating element ?"
You will have to reinforce the cable to at least a 10mm Two Core and Earth if it already isn't.
The reason the fuse hasn't blown is more than likely to be that it is a rewireable fuse with the wrong size fuse wire in it. An MCB (miniature circuit breaker) would not have been able to take the current load and would have tripped off at the first switch on of the shower.
You consumer unit (fuse box) is rated at 60 amps on the main switch and BUS bar and you should probably never reach this load even with everything in the house switched on.
More information about the whole installation as it is now, would help us make a better diagnosis of any problems you may get if you go ahead with the your proposed changes.