To me, it appears the grey cable feeds the little fusebox, and could only be 4.0mm.
White cables are the outgoing circuits to whatever it’s supplying.
If it’s an easy route back to the board, best to put the shower on its own circuit, protected by rcd and an isolator switch before going to the shower.
Ideally, and to comply with Part P building regs, you should get an electrician to design, install and test this circuit…. It could be a much bigger job than you think if there’s no rcd at the board.