If an appliance uses more than 2 kW and is not portable, appendix 15 of BS 7671 suggests one way to stop overload for a long period is to use a dedicated supply.
Since my tumble drier uses 600 watt, it does not need a dedicated supply, and most modern heat pump tumble driers will not need a dedicated supply.
Even my old vented tumble drier had two options 1 kW or 2 kW, it would trip out on overheat on 2 kW setting so always used on 1 kW setting. And so did not need a dedicated supply. And even at 2 kW it would be right on the limit, so still some debate as to if it needs a dedicated supply, and the regulations say "This can generally be achieved by:" it does not say you must use that method.
The problem is down to getting the heat away from a plug, and not overloading one end of a ring final, if the socket is reasonably central on the ring final then no problem with overload. As to the plug, if supplied with the machine, it should be of a colour and type able to remove the heat if in free air, the problem is when the socket is under a counter top, so not in free air, and the plug is hidden from view, so any signs of over heating is hidden from the user.
Plugs and sockets are designed to be unplugged and plugged back in, and the action of doing this cleans the pins, as to if required, depends on what the contact surface is made from, so no regulations says they must be unplugged after use.
As to tumble drier fires, must are caused by bad design or poor maintenance, which results in a build up of fluff on the heating element, I am sure someone can find somewhere a report of a modern heat pump drier going on fire, but I do not know of any.
As to sharing a socket with a washing machine, yes double socket rated at 20 amp not 26 amp on a continuous basis, the element in the washing machine likely only works for 5 minutes, so not really a continuous basis, and since most washing machines are on wheels, they are classed as portable in spite of their weight.
