Braden started her career alongside her parents in the 1960s on the British television series The Rolling Stones and B and B. She had a supporting role in the adventure movie Wolfshead: The Legend of Robin Hood (1969) and portrayed Joan Crawford's daughter in the horror film Trog (1970). Braden acted as Anne Shirley in the television mini series Anne of Green Gables (1972) and Anne of Avonlea (1975) and had guest roles in episodes of Justice (1971), Armchair Theatre (1973), Z Cars (1973), Laugh-In (1977), Penmarric (1979), and ITV Playhouse (1980).