The formal process of legal adoption did not come into force until 1927. Prior to that date, the most common form of "adoption" was within the family - an child born to an unmarried mother might be passed of as her own mother's or as that of a married sister, or simply to an aunt or cousin (or even a friend or neighbour) who had no children of her own. Have you thoroughly researched the Chalk family to see if there is a connection? Did they have any other children?
If the mother was unable to make such an arrangement, or to keep her child, churches and charities might try and find a home for it, either directly after birth or after a period in an institution. Was Laura born away from the family home? If so, was her mother taken in by a charitable body?
After the Adoption Act came into force it was possible for parents who had "adopted" children earlier to seek to formalise the arrangement through a court order. If this was the case with your family member her birth certificate should be annotated with the word "adopted" and she would have been issued with an "adoption certificate" (which is indistinguishable from a short form birth certificate) in her new name.
Hope this helps