Cooper is a vice-president of the Putney and Roehampton Branch of the United Nations Association, and chairs the Wandsworth Co-op Party.

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 the 2024 London Assembly Election, Cooper was re-elected with 77,235 votes, a 27,423 majority over Ellie Cox, the Conservative Party candidate.

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.