Second World War Mitchell was recruited to work at
Bletchley Park in September 1943 after she graduated from Oxford, and until May 1945 she worked in
Hut 6 on German Army and Air Force
Enigma decryptions. Much of her work involved converting 'cribs' into 'menus', the operating instructions for the
Bombe decryption devices, to identify what that day's Enigma settings might be. The Germans changed their code every night at midnight, so Mitchell and the others had then to restart trying to crack the codes. Stuart Milner-Barry, the head of Hut 6, had difficulty recruiting enough men due to war demands and British civil service rules prevented men and women from working together on night shifts, so Mitchell worked solely with women in Hut 6. After the war, like others who worked at Bletchley, she was instructed to forget about her work there and never to talk about it. Once the work at Bletchley became public and the ban was lifted she gave many illustrated talks and interviews about her wartime role. Her story is included in the book
The Bletchley Girls: War, Secrecy, Love and Loss: The Women of Bletchley Park Tell Their Story (2015) by the historian
Tessa Dunlop. In the 1970s she returned to university to study social policy and in 1980, she graduated with a Master of Philosophy from the
University of Edinburgh. Mitchell worked and published extensively on the subject of marriage breakup and divorce, and in particular on children's experience of family breakup. Her books include
Someone to Turn To: Experiences of Help before Divorce (1981);
When Parents Split Up (1982);
Children in the Middle (1985);
Coping with Separation and Divorce (1986); and
Families (1987). They have been translated into a number of languages. Mitchell's work is referred to in several works on divorce in Scotland and further afield, and was used as supporting evidence in two reports by the
Scottish Law Commission, "Family Law: Report on Aliment and Financial Provision" (1981) and "Report on Reform of the Ground for Divorce" (1989). In 2014, in an article in the
Scots Law Times, the
family law barrister Janys Scott
QC reviewed Mitchell's work on the workings of the Scottish divorce court. Scott concluded that "Mitchell has had a profound influence on family law in Scotland", and that her 1985 book
Children in the Middle was "a seminal work" in the field. and ''No More
Corncraiks:
Lord Moray's
Feuars in
Edinburgh's New Town'' (1998). ==Personal life==