6mm will carry 47A under reference method C, which is both clipped direct AND/OR embedded in plaster. It will carry 41 under method B which is conduit or trunking either on surface or embedded.
An 8.5kW shower pulls 36.9A at nominal voltage. Round 'ere, voltage is usually closer to 240 which, in the real world, brings this figure down even further. The only place we are really going to have problems with this is when the cable is run through thermal insulation (meth A), which gives us only 34A, and decreases with similar methods (100, 101, 102, 103 etc).
For the record, if they are upgrading to an 8.5 on 6mm, and I can't see presence of insulation in the run, I will put the shower on this cable with a 40A breaker (and RCD of course), but if I was installing the shower from scratch, then I woud put in a 10mm.
This is my interpretaion, anyway, please let me know if I am wrong.