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Banks was born in Enfield Highway, Middlesex, the only child of Herbert Alfred Davies and Jessie Louise (nee) Tebby. She married Joseph Ambrose (Joe) Banks in June 1944 and they both entered the London School of Economics to study sociology. Her PhD thesis was turned into her first book, Parity and Prestige in English Secondary Education: a Study in Educational Sociology (1955).
In 1954 she accepted a research post at Liverpool University, where she was able to investigate the history of British feminism, culminating in the publishing of Feminism and Family Planning in Victorian England (1964). Her reputation as a leading scholar in her field was sealed with the publication of The Sociology of Education (1965).
Following her retirement in 1982, she continued her research, publishing a two volume Biographical Dictionary of British Feminists (1985-1990) and Becoming Feminist: The Social Origins of 'First Wave' feminism (1986). The Politics of British Feminism (1993) was her last book.