Meadley was born at Sunderland, County Durham, on 1 January 1774, an only son; his father died in 1775, and his mother soon afterwards moved with her five children to the adjoining town of Bishop Wearmouth.
At the end of 1788 he was apprenticed to Thomas Chipchase, a banker and general dealer at Durham, where Meadley became a liberal in politics.
Learning German, he went on further mercantile voyages to Danzig (1801) and to Hamburg (1803), travelling further on foot with a friend through northern Germany.
Several years later he began to collect materials, applying, among others, to John Disney, who introduced him to Thomas Jervis; as a by-product he became a Unitarian.
When bringing out a second and amended edition (1810) he spent the winter in Edinburgh to see it through the press, and attended the moral philosophy lectures of Thomas Brown.