Fenemore played mainly supporting roles which were characterised in her obituary in The Stage as "friends, neighbours, mothers and passers-by"; however, her many credits meant that she fell into the category of actresses who a majority of film and TV viewers would have been unable to name, yet whose face was instantly recognisable.

Fenemore began her career as a stage actress, joining the company of actors at London's left-wing and progressive Unity Theatre in the 1940s.

At the end of the 1950s, Fenemore appeared in two of the early Carry On films, notably in a memorable, albeit brief, cameo in Carry On Nurse (1959) as a wife visiting her husband in hospital, supremely oblivious to the absurdly snobbish impression of upper middle class gentility he has been trying to give his fellow patients, and blithely broadcasting embarrassingly working class trivia at full volume to the entire ward ("I bought this with our divi from the Co-op!")

1961 brought one of Fenemore's more prominent screen credits, portraying the matriarch of the family at the centre of The Wind of Change, one of the first British films to confront the issue of contemporary race relations.

She also starred in the cult favourite CFF production Chico the Rainmaker, originally shown as a serial during children's Saturday cinema matinees in the UK, and later on PBS in the United States.