A double socket is not actually safe to run two 13a appliances at the same time. I believe the design current is about 20A.
The original thinking (going back to the 1940's) was that a person with a double socket might plug in one heavy load (e.g. an electric fire or a washing machine) and use the other for a light load (e.g. a table lamp or a wireless set). It was not thought that anyone would have two washing machines in the same room, or two electric fires next to each other. At the time people had far fewer electric appliances than today, and almost none of them were as high as 10Amps load.
The thought processes are still fairly correct; except in a kitchen, where people now have a multiplicity of heavy loads (dishwasher, washing machine, tumble drier, combination microwave) that can be about 13A each. So for your single large undercounter appliances, one switch and one single socket are preferable. For your overcounter appliances, like the kettle and toaster which are only on for short periods, or the food processor and juicer, double sockets are fine, and the more the better.
I did see a lab report (might have been by MK) on a double socket with two continuous 13A loads on it; it overheated quickly, soon started to smell and became permanently damaged. Fortunately, a lot of heavy load appliances (e.g. many single ovens) are only 10A each, and have intermittent loads, so you can use two of them in a double socket without it melting.