Tillyard was born in Cambridge as the second child and only daughter of local newspaper proprietor/editor Alfred Isaac Tillyard MA and his wife Catharine Sarah née Wetenhall, proponent of higher education for women. Her mother was one of the first women to take the Higher Local Examination after attending lectures for women in Cambridge. Tillyard had three brothers, one of whom predeceased her; Henry Julius Wetenhall Tillyard (1881-1968), classicist and expert in Byzantine Musicology, Conrad Francis Wetenhall Tillyard (1885-1888) and Eustace Mandeville Wetenhall Tillyard (1889-1961), active in English Literature studies and Master of Jesus College, Cambridge.
Born in Cambridge as the second child and only daughter of local newspaper proprietor/editor Alfred Isaac Tillyard MA and his wife Catharine Sarah née Wetenhall, who promoted women's higher education, Tillyard had three brothers: Henry Julius Wetenhall Tillyard (1881-1968), a classical musicologist; Conrad Francis Wetenhall Tillyard (1885-1888); and Eustace Mandeville Wetenhall Tillyard (1889-1961). All three brothers were involved in English literature studies, with the latter becoming Master of Jesus College, Cambridge.