The Bluetts traced their pedigree back to an early medieval earl of Salisbury, though the veracity of this claim is difficult to determine. They came to prominence first in Somerset, providing knights of the shire in at least four Parliaments during the 1300s. However, during the following century they acquired by marriage the Devon manors of Holcombe Rogus and Wobernford, respectively nine and three miles from Tiverton.
Bluett was aged only nine when his father died in 1612. Now heir to the family estates, which comprised 16 manors in Somerset, Devon and Dorset, he became a royal ward upon the death of his grandfather three years later. His sisters were entrusted to the care of their mother and her recusant second husband, but Bluett’s wardship was acquired by the fervently Protestant Arthur Chichester, lord deputy of Ireland.
