In 1642 Greaves had been elected subwarden of Merton College. Merton was the only Oxford college to side with the Parliamentarians in the English Civil War, through an earlier dispute in 1638 between Nathaniel Brent, the Warden of Merton, and Greaves' patron William Laud. Brent had been a witness for the prosecution at Laud's 1644 trial. After Laud was executed on 10 January 1645, Greaves drew up a petition for Brent's removal from office; Brent was deposed by Charles I on 27 January.