He was the grandson of Sir Edward Coke, Lord Chief Justice.
His father Clement (died 1629), youngest son of Sir Edward, acquired by marriage the Longford Hall estate in Derbyshire.
Coke served as high sheriff of Derbyshire in 1646.
His son, the 2nd Baronet, was Member of Parliament for Derbyshire in 1685.
The Longford estate passed into the ownership of the senior branch of the Coke family of Holkham Hall, Norfolk, represented by the Earl of Leicester.