It includes Balham High Road, Streatham High Road, and Colliers Wood High Street.
A consultation has started on the plans, which the Mayor of London says will reduce death and serious injury on the roads.
A 20mph limit would be introduced on sections of the following roads:
A205: Woolwich Common, South Circular Road, Catford Road, Stanstead Road, London Road, Thurlow Road, Christchurch Road, Poynders Road, Dulwich Common
A20: Eltham Road, Lee High Road, Lewisham Way
A202: Queens Road, Peckham High Street, Camberwell Church Street, Camberwell New Road
A2: New Cross Road, Old Kent Road
A201: New Kent Road
A100: Tower Bridge Road
A200: Jamaica Road
A3: Clapham Road, Kennington Park Road
A3204: Kennington Lane
A203: Stockwell Road
A23: Camberwell New Road, Streatham Hill, Streatham High Road
A214: Tooting Bec Road
A24: Clapham Common South Side, Balham High Road, Upper Tooting Road, High Street Colliers Wood
A4: Cromwell Road, Brompton Road
A3220: Pembroke Road, Holland Road, Warwick Road, Redcliffe Gardens
A232: West Wickham High Street