He went to school at a private academy near London, and when sixteen years old at his own request was apprenticed to Savory & Moore, the chemists and druggists, in which he later purchased a partnership.
From Naples he went through Styria and Carniola to Vienna, made an excursion through Poland and Russia, and returned home by way of Hamburg.
Davidson went to Egypt at the end of 1829, visited the Pyramids, and passed overland to Cosseir, where he embarked for India on his way to China and Persia.
He undertook to head an African expedition, at his own expense, and proposed to proceed by way of Fez to Tâfilêlt, and then via the southern slope of Mount Atlas, to Nigritia, across the Sahara.
He started for the great desert at the end of November 1836, but while stopping at a watering-place called Swekeza he was robbed and murdered on 18 December 1836 by the tribe El Harib.