Green’s Dictionary of Slang

the rejection of a suitor.

1909

J. Ware Passing Eng. of the Victorian Era 252/1: Turnups (Lower Peoples’). Rejection of a suitor. She dismisses him – or turns him up – said to be from hospital practice of turning up the ordinary joint bedstead when a patient left it for the grave. Corrupted into an idea of turnips – generally pronounced turnups by the vulgar.