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Given that parents in English speaking countries have always had complete freedom to name their children whatever they want, it's hard to say that any particular name would be "impossible." However, it is extremely unlikely that a woman born in the early 19th century in England(in order to be an "old lady" in the late 19th century)would have Kelly as a given name. Of course, Kelly was a surname back then, and servants of both genders were often addressed by their surnames by their employers. So having an employer address a female maid or a cook "Kelly" might have been possible, but it would have been her surname, not her given name, that was being used.

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Bennett would be about as unlikely as Kelly as a given name. Shirley would have been somewhat possible. Even if this is a "working class" girl, not all working class parents were illiterate, and even if they were, there's always the possibility of an employer or other educated acquaintance suggesting the name, or of them hearing it being used as a child's name for a middle class girl and adopting it in that way. However, Leslie Dunkling's The Guinness Book of Names has Shirley first being used enough to be noticeable in England in 1861, so before then it must have been quite rare. He doesn't have Kelly being regularly in use in England until 1958.