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.
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, advocate of women's higher education. She had three brothers, one who preceded her; Henry Julius Wetenhall Tillyard (1881-1968), expert in classical musicology, Conrad Francis Wetenhall Tillyard (1885-1888) and Eustace Mandeville Wetenhall Tillyard (1889-1961), engaged in English literature studies and Master of Jesus College, Cambridge.