If I have a steam room shower, that is run off water, but I need an electric cable to feed the steamer and the light inside, the shower is 3KW and in an en suite bathroom. What size cable and what size fuse would I need??

You don't need a fuse , you need a 50 amp GFI breaker. I'd need to know the heater draw but #10 wire would be in the ball park. Is this room inside or out of doors?