His eldest son, Joseph Cappe, M.D., died in February 1791; his youngest son, Robert Cappe, M.D., died on 16 November 1802 while on a voyage to Livorno, Tuscany.
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An earlier sermon delivered 27 November 1757, after the victory of Frederick the Great at the battle of Rossbach on 5 November 1757, was of a very rhetorical character and passed through numerous editions.
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His second wife, an ardent promoter of education and of unitarian principles, was Catharine, daughter of the Rev. Jeremiah Harrison, vicar of Catterick, North Yorkshire, and they were married at Barwick-in-Elmet, Leeds, on 19 February 1788.