Wandsworth council launched the scheme in the summer holidays last in partnership with Places Leisure.
It extended the initiative on 1st January to include residents claiming a wider range of benefits, including 17 and 18-year-olds receiving free school meals.
Leisure facilities in Wandsworth managed by Enable have also been added to the offer, including Battersea Sports Centre, Barn Elms Sports Centre and Tooting Bec Athletics Track and Gym.