The second child of Roger Kemble – the manager of the travelling theatre company the Warwickshire Company of Comedians – he was born at Prescot, Lancashire. His mother being a Roman Catholic, he was educated at Sedgley Park Catholic seminary (now Park Hall Hotel), near Wolverhampton, and the English college at Douai, France, with a view to becoming a priest. At the end of the four years' course, he still felt no vocation for the priesthood, and returning to England he joined the theatrical company of Crump & Chamberlain, his first appearance being as
Theodosius in Nathaniel Lee's tragedy of that name at Wolverhampton on 8 January 1776.
In 1778, Kemble joined the York company of Tate Wilkinson, appearing at Wakefield as Captain Plume in George Farquhar's The Recruiting Officer; in Hull for the first time as Macbeth on 30 October, and in York as Orestes in Ambrose Philips's Distresset Mother. In 1781 he obtained a "star" engagement at Dublin making his first appearance there on 2 November as Hamlet. He also achieved great success as Raymond in The Count of Narbonne, a play taken from Horace Walpole's The Castle of Otranto.