RCD is a safety device which will trip the supply if an electrical fault (Short etc) is detected.
The cable diameter is dependant on both the length of cable run (Supply connection to the Shower) as well as the actual load - the wattage of the Shower e.g. 9.6Kw)
I would agree with previous posts that it is likely to be the thermostat or conection to the element. The fact that the water is still running means power must be on for the valve to be open.
If you are not sure about this seek professional advice - as previously stated this can be a very dangerous area to work on.