Actually 10A. A lot of them have this restriction. 10A continuous and 13A (or even 16A) intermittently. You even also find this restriction on the wall outlets where the cheaper ones tend to be rated at 10A continuous even though they are marked as 13A. This is very dodgy practice so if your purchasing outlets or smart switches for high current loads make sure the continuous rating is at least 13A.
My Granny charger will only drawer 10A as do most washing machines and tumble driers (rated at 2.2kW not 3kW) which I'm sure is a response to the poor control of the specification for socket outlets. These loads are continuous. Kettles are sometimes 3kW rated but these are considered to be intermittent loads (2 minutes at a time). If you boil lots of water with a 3kW kettle in quick succession have a feel of the cable and plug afterwards. They are worryingly warm. When I fitted my socket outlets for the charger I made sure they were 13A rated even though only 10A was needed.
The smart plug is suppose to detect if it is overloaded and disconnect the load but in the case of the Tumble Drier fire this obviously didn't work.