Kennedy attended the University of Warwick between 1988 and 1991, gaining a BSc in psychology.

She then worked for the party's central organisation, including as Chief of Staff, 2001–2005 and Deputy General Secretary, 2006–2011.

In July 2021, in the wake of the Covid crisis, she and Lord Bird of Notting Hill called for an end to section 21 evictions in the private rental sector.

[4] In the House of Lords she was a member of Joint Committee on the Draft Modern Slavery Bill which examined the proposals from the Government and presently serves on the Affordable Childcare Committee.

[5] In 2014 she was elected as a councillor in the London Borough of Lewisham representing Brockley.