Are standard UK wall sockets a 16A power supply
BS1363 is 13A max

The UK BS1363 plug system is 13A, maximum, per receptacle.  Since your appliance does not support that setting, only 10A and 16A, the 10A setting is correct; furthermore, they were smart enough to fuse the plug properly (at 10A) -- this means that if you tried to set it to 16A, you'd eventually blow the fuse in the plug.