In the 1992 general election Cooper contested Hornchurch, coming second to the Conservative incumbent, Robin Squire. Cooper was first elected to Wandsworth Borough Council in 2006, as a Councillor for the Latchmere Ward in Battersea. In 2010, she was elected as a Councillor for the Furzedown Ward in Tooting, re-elected in 2014. When Cooper was selected in 2009 for Furzedown it was a marginal Ward, with Conservative and Labour Councillors. Since 2010, Cooper has enjoyed the largest majority of any Wandsworth Labour Councillor, receiving more than three thousand votes in 2010, 2014 and 2018. In 2008 and 2012, Cooper contested the Merton and Wandsworth Assembly seat, losing on both occasions to Richard Tracey, although achieving an increase in the Labour vote of 5.2% and 7.5% respectively. In May 2016, Cooper defeated the Conservative candidate to become the first Labour representative for Merton and Wandsworth since the establishment of the London Assembly. This was the only constituency Assembly seat to change hands in the May 2016 elections. At the London Assembly Annual Meeting on 13 May 2016 Cooper was confirmed as the new Chair of the Assembly's Environment Committee 2016-18, and as a member of the Assembly's Housing Committee. Cooper was the first of the 2016 intake of Assembly Members to gain agreement for a single-member led investigation, producing her report on "Biodiversity in the new housing developments" in January 2017. The Environment Committee has already produced a number of reports under her leadership, on single-use plastic bottles, on domestic energy and fuel poverty and on parks and open spaces. These were all submitted to the Mayor prior to the launch of the Mayor's draft Environment Strategy in August 2017, and many of their recommendations now feature in it. In addition, the Mayor's draft London Plan refers to both net biodiversity gain and an Urban Greening Factor, both recommendations from Cooper's report on "Biodiversity in new housing developments". Cooper currently serves as Chair of the London Assembly's Economy Committee, and Deputy Chair of the Environment Committee. She is the London Assembly Labour Group's lead spokesperson on the economy. In June 2019, she launched a new report, 'Running Out or Flooded Out?', investigating the impact of water leaks, drought and flooding on London.