Following her graduation from Pembroke College, Cox worked as an adviser to Labour MP Joan Walley from 1995 to 1997. She then became head of Key Campaigns at Britain in Europe (1998–99), a pro-European pressure group, before moving to Brussels to spend two years as an assistant to Glenys Kinnock, wife of former Labour leader Neil Kinnock, who was then a Member of the European Parliament.
