Fitzwilliam was educated at Magdalen College, Oxford, where he entered as a servitor in 1651, and was elected to a demyship in the same year. At the Restoration, according to Anthony à Wood, ‘he turned about and became a great complier to the restored liturgy.’ But Fitzwilliam himself appeals to ‘the zeal I had for the present government even while it was merely to be enjoyed in hopes, and we could only wish it might be restored’ (sermon preached in 1683). In 1661 he was elected fellow of Magdalen, and held his fellowship until 1670. He was made librarian of the college in 1662, being at the same time university lecturer on music. His first patron was Dr. George Morley, afterwards bishop of Winchester, who recommended him to the lord treasurer, Thomas Wriothesley, the virtuous earl of Southampton, in 1664, in whose family he resided as chaplain, and instructed Lady Rachel Wriothesley and her sisters. On the death of the Earl of Southampton Bishop Morley ‘took him into his own household,’ and on ‘his dismission from his service with a fair reward’ recommended him in 1666 as chaplain to the Duke of York, afterwards James II, to whose daughter, the Princess Anne, he became tutor. In 1669 he was appointed by Bishop Morley to the living of Brightstone in the Isle of Wight, on the resignation of Dr. Thomas Ken, who was collated to the living of Woodhay. He was afterwards presented by his friend, Bishop Turner of Ely, to the living of Cottenham, near Cambridge, and promoted by the crown to a canonry at Windsor in 1688. He was a friend both of Thomas Ken and of his brother-in-law, Izaak Walton, who sent him presentation copies of all his works. He was also on terms of intimacy with John Kettlewell. He attended, with Ken, Bishop Morley's deathbed in 1684. At the Revolution he resigned his preferments, because his conscience forbad him to take the oaths of allegiance to the new dynasty.