He was the eldest son and heir of Sir Thomas Speke (1507-1551) of Whitelackington, MP for Somerset in 1545, twice Sheriff of Somerset and Dorset in 1540 and 1550, and a Gentleman of the Privy Chamber to King Edward VI.
His mother (his father's 1st wife) was Alice Berkeley, daughter of Richard Berkeley and sister of Sir Maurice Berkeley.
[1] He succeeded his father in 1551 and was knighted in 1559.
He was elected a Member of Parliament for Somerset in 1572.
He married twice:[2] He was succeeded by his eldest son Sir George Speke, of Whitelackington, who married Phillippa Rosewell, daughter of William Rosewell, Solicitor General.