the major factor in your question is the length of the run of the cable. 9.5 kw is a reasonable amount of power to draw. If the run is to long you risk considerable voltage drop. you need to look in the on site guide, published by the i.e.e. this will give you all of the correct sizes for cables. etc. A bathroom is classed as a special location, so make sure your main bonding is up to scratch (on site guide) also your supplementry bonding. Do you have a local isolation switch. ( if so is it in the correct location) Is this circuit protected by an R.C.D.? It may have to be depending on many factors.
But generally i would say 6mm is insufficient. Remember if you get it wrong, the cable can become the fuse, Very bad = fire. or under fault conditions a 40 amp or so shock will turn you into a big smelly lump of charcoal. i.e dead.
On site guide is the way forward. go to any book shop in the technical section. you must considder the resistance of the cable is determined by its length and c.s.a. then the wattage of the appliance. once you have these simple figures, you just look it under the relevent table in the book.
or get an electrician.
you will probably end up using 10 or 12mm cable. check you can terminate this in the shower, as normally they can be a real pig.
remember dad doesn't always know best
jim, March 2007