Richardson only mentions St Leger in passing due to John's marriage to Margery Donet. RA4, p. 460-1: "She married John Saint Leger, Esq., of Ulcombe, Kent, Sheriff of Kent, 1430-1, and in right of his wife, of Silehan (in Rainham), Kent, son of Ralph Saint Leger." He cites the The Visitation of Kent by Benolte & Cooke which has a St Leger pedigree that starts with John St Leger, p. 68. He also cites Hasted's The history and topographical survey of the county of Kent, Vol. 6, p. 9 which mentions the marriage. There is actually more information in Hasted, Vol. 5, p. 389 (link, link), which in a typically ambiguous manor says:
Ralph St. Leger possessed this manor in the reign of Edward III. when he paid aid for it, as two knights fees, held of the archbishop; in which year he represented this county in parliament. His youngest son, Thomas, was of Otterden, where a further account may be seen of him. Arnold St. Leger, the eldest son, succeeded his father at Ulcomb, and represented this county in parliament, as did his son Ralph St. Leger, esq. of Ulcomb, and in the 10th year of Richard II. was sheriff of it. His son John St. Leger. esq. was of Ulcomb, and was likewise sheriff, anno 9 Henry VI. three years after which, he was returned in the list then taken of the gentry in this county, who had a right to bear the coat armour of their ancestors. He died anno 20 Henry VI. possessed of this manor, and was buried in this church. He left three sons; Ralph, who succeeded him at Ulcomb; Sir Thomas, who married Anne, duchess of Exeter, and left a sole daughter and heir, married to Sir George Manners, lord Ross, ancestor of the earls and dukes of Rutland; and Sir James St. Leger, who married Anne, daughter and coheir of Thomas Butler, earl of Ormond, from whom the St.Legers, of Devonshire, are descended.
I didn't see anything about Arnold's wife or John's mother in these references.