Anneliese was born and brought up in North East Scotland, before leaving home to attend University in Oxford. For many years she worked as an academic, first at the London School of Economics and then at King's College London, and latterly at Aston University. This included working as the Acting Director of the NIHR Research Centre on Patient Safety and Service Quality joint between KCL and KCH, and also as a visiting professor at the University of Prishtina (Kosovo).

Anneliese served as a Labour Member of the European Parliament for the South East of England between 2014 and 2017, where she sat on the Committee for Economic and Monetary Affairs, and represented the Socialists and Democrats on a number of packages concerning financial regulation and tax avoidance and evasion.

In 2017 Anneliese was elected as the MP for Oxford East, and soon after became a shadow Treasury minister. In April 2020 she was appointed Shadow Chancellor of the Exchequer. Anneliese has also served as the Chair of a debt and welfare advice centre on the council estate where she lives with her family (Rose Hill).