'Scuse me butting in, but I'd like to test my own rudimentary understanding of what's going on here.
If one took a pessimistic view of your 6mm^2 cable cable run, such that it were classed as running all the way "in conduit in thermal insulation", then it would be rated at 34.0A. An 8.5kW shower would require 35.4A at 240V, so the cable is not adequate for sustained operation.
10mm^2 cable, in the same conditions, could sustain 46.0A, which is enough for your shower.
I don't know how to determine the correct breaker for this scenario, but clearly it would have to be rated at more than 35.4A and less than 46.0A.
I've also seen mention of considering the length of the cable run to determine the voltage drop from supply to appliance. However, I don't claim to know what the permitted, or advisable, limit is on the amount of the drop.
Have I got this right?