Hi Teach,
Welcome to the forum.
I would take issue with your remark that socket outlets (other than SELV or shaver) are permitted in bathrooms under controlled circumstances in installations wired in accordance with BS7671: 2001. See Reg 601-08-01.
RCD protected sockets are permitted outside zone 3 where a shower cubicle is fitted in a room other than a bathroom or shower room, eg. a bedroom. See Reg 601-08-02.
Washers & dryers can certainly be installed in a bathroom providing they are permanently connected & suitable for the zone they are installed in, with RCD protection where required.