Sir Algernon May (? - 25 July 1704) was an English member of Parliament, for the constituency of Windsor, in the late 17th century. He was the fifth son of Sir Humphrey May of Carrow Priory in Norfolk, Chancellor of the Duchy of Lancaster, 1618-1630. A fortunate marriage in 1662 to Dorothy Reynolds, the widow of a Cromwellian soldier, James Calthorpe, brought him the Suffolk manor of Ampton, as well as lands in Ireland. He was Equerry to Catherine of Braganza from 1662 to 1668, and Keeper of the Records in the Tower of London from 1669 to 1686.