It exists in dreams and half life. Arthur is destined to return when Britain needs him the most. There are numerous novels about his death and fantasies of his return. Merlin was long gone when Arthur fought Mordred and was mortally wounded. read more
Of course, they could have assumed his death when Merlin does not return. But that would take a long time, you don't want to proclaim a king, who's known to go on adventure from time to time, dead after a few weeks. The coronation scene does not seem to imply it was very long after the battle, though that's more of an educated guess. read more