I think it does lay horizontally across ceilings, but that is still 'Method C' (aka 'clipped direct').Winston made a statement without mentioning / considering the method of installation. Maybe the cable is clipped direct to a wall and doesn't have any section of it laying horizontally across a ceiling ....
No-one has suggested 4mm² cable - the OP already has 6mm², and that is almost certainly quite adequate.... in which case 4 mm² might be OK But dropping almost 5 volts at 37 amps is 180 watts about 2 % of the power measured by the meter and thus paid for is being wasted in heating the cable..
Are you seriously suggesting that anyone would go to the tremendous hassle of wiring an 8.5kW shower with 16mm² cable, just to avoid a small amount of energy loss in a cable for a few minutes per day?
Kind Regards, John