Many people have.
There is a lot of debate/argument as to what the 'rating' (maximum current between both outlets) of a double socket is. Some assume that it is 26A (i.e. 2 x 13A), but others say that it is only 20A, that stemming from the fact that the Standard for such products requires that they pass a 'temperature rise test' when a total of 20A is being drawn .
However, for a start, I don't think many combinations of dryer + washing machine would actually ever draw more than 20A (I don't think mine ever would/could), but the fact is that we do see reports of plugs/sockets overheating, sometimes to the point of showing appreciable damage, when two such machines had been plugged into the same double socket. On the other hand, many people have had that arrangement operating for years, without any problems.
As far as "acceptable to the authorities" is concerned, the Wiring Regulations are only really concerned with the fixed wiring (which includes the installation of a double socket) - and do not (and really could not) directly concern themselves with what a householder might subsequently plug into that socket. I suppose that an electrician who believed that two such machines would be plugged into it might refuse to install the socket if he/she had been told of that intent - but even if he/she had been told that the intent was something different (and 'acceptable'), then there would be nothing stopping the (same or subsequent) householder plugging in whatever he/she liked.
Kind Regards, John