Speke came from a cadet branch of the Somerset family that acquired Hazelbury in 1602. The family connexions were entirely Roman Catholic, and Speke was educated at Douai, where his uncle Francis had entered the novitiate some years earlier. Speke’s mother and sister were presented as recusants in 1644, but his father was a man of discretion who preserved his estates by his prudence throughout the Civil War. Speke also conformed, and married ‘a rigid sectarist’, related to the leading puritan families of Buckinghamshire, who brought him a substantial estate in Kent.4G. J. Kidston, Manor of Hazelbury, 191-8, 235-9; CSP Dom. July-Sept. 1683, p. 212.
At the Restoration Speke obtained a baronetcy and a place at Court. He was involved in a double return for Chippenham, five miles from his residence, at the general election of 1661. The rival candidates were originally seated on the merits of the return, but the election was declared void, and at the ensuing by-election Speke was successful. But he died five days later, probably before taking his seat.5Bath mss, Thynne pprs. 10, f. 108; CJ, viii. 253.