Her father, then a captain in the Royal Navy, was frequently reposted, both around the UK and for two years in Washington DC, so Anna and her sisters were educated at several different schools.
Coote played an important role in bringing about student reforms and the resignation of Malcolm Muggeridge, the Rector of the university, in 1968.
Muggeridge attacked the motion for promoting promiscuity and announced his resignation from the pulpit of St Giles' Cathedral in January 1968.
[6] Diverse was set up to pioneer programming on politics and current affairs to the new Channel 4 based on tough journalistic standards.
From 1998 to 2004 she was Director of Health Policy at the King's Fund; and from 2005-08 she led the Healthcare Commission’s work on engaging patients and the public.
Her publications during this period covered a wide spread of topics, including the potential of citizens' juries, the politics of gender, social rights, and inequalities in health.
In 2000 Coote was appointed a member of the UK Sustainable Development Commission, which she held until shortly before 2010 when the SDC was abolished by the incoming Coalition government in the "bonfire of quangos".