There is no direct connection from Chiswick to Brixton. However, you can take the Tube to Victoria Underground Station then take the Tube to Brixton Underground Station. Alternatively, you can travel from Chiswick to Brixton in around 20 min.
From Chiswick Park Underground Station Tube to Victoria Underground Station then Tube to Brixton Underground Station. 30 min £3. From Chiswick taxi to Brixton. 20 min £41. From Chiswick drive to Brixton. 20 min £1. From Chiswick Uber to Brixton. 20 min £20. From Chiswick walk to Brixton. 2 h 43 min. From Ravenscourt Park Station, Hammersmith Bikeshare to Clapham Road, Lingham Street, Stockwell. 45 min.