[1] Having been educated in grammar learning by Thomas Farnabie, he became a commoner of Trinity College, Oxford, in Midsummer term 1633, and was admitted scholar on 28 May 1635.
He joined with Henry Stubbe, of Christ Church, Oxford in publishing another volume of Latin verse in the same year.
[2] Birkhead also edited, with a preface, some philological works of Henry Jacob the younger in 1652; and wrote several royalist Latin elegies to persons who had suffered for their devotion to Charles I.
[3] Birkhead was one of the contributors to this collection, which included elegies by Jasper Mayne, William Cartwright, Dudley Digges, and others.
Forty-one years afterward, in 1684, the collection was reprinted, and Birkhead, the only survivor save one of the thirteen contributors, addressed a long 'Epistle Dedicatory' to John Granville, 1st Earl of Bath, son of Sir Bevill Grenvill.