The Pit-Prop Syndicate by Freeman Wills Crofts

Though Inspector Willis had spent so much time out of London in his following up of the case, he had by no means lost sight of Madeleine Coburn and Merriman. The girl, he knew, was still staying with her aunt at Eastbourne, and the local police authorities, from whom he got his information, believed that her youth and health were reasserting themselves, and that she was rapidly recovering from the shock of her father's tragic death. Merriman haunted the town. He practically lived at the George, going up and down daily to his office, and spending as many of his evenings and his Sundays at Mrs. Luttrell's as he dared.

But though the young man had worn himself almost to a shadow by his efforts, he felt that the realisation of his hopes was as far off as ever. Madeleine had told him that she would not marry him until the mystery of her father's murder was cleared up and the guilty parties brought to justice, and he was becoming more and more afraid that she would keep her word. In vain he implored her to consider the living rather than the dead, and not to wreck his life and her own for what, after all, was but a sentiment.