The son of William Brooke, 10th Baron Cobham, by second wife Frances, daughter of Sir John Newton, he was educated at King's College, Cambridge.
His brother George was executed, and Henry was imprisoned in the Tower of London by James I, probably in an attempt to obtain the Cobham estates for the Duke of Lennox.
He may have been the subject of a number of Elizabethan satires such as Thomas Nashe's Lenten Stuffe, Ben Jonson's Every Man in his Humour, and may have been the model of Shakespeare's Falstaff, who was originally given the name "Oldcastle".
Although Falstaff is more likely modelled on his father, William Brooke, 10th Baron Cobham (also descended from John Oldcastle), who was married to Frances Newton, whose family name was originally Caradock; referenced in Henry IV, Part 2 when Falstaff sings The Boy and the Mantle, a ballad in which Sir Caradoc's wife comes away with her fidelity and reputation intact (McKeen 1981).
At the very same time, Grey and Cobham entered into the Main Plot to raise a regiment of soldiers and force a coup d'etat.
Cobham and Grey were to raise one-hundred and sixty thousand pounds (a figure that could be safely multiplied by twenty to convert to contemporary money) to bribe or hire an army.