Insp. Henry Scarlet tells young Wellington that he signed up for the police force on November 10, 1848, 24 years ago. This means Eliza and William met in 1872 when she was 16, and that it is now 1884, 12 years after they met.
The Duke's full name is William James Wellington, and he was discharged from a workhouse in Glasgow before he came down to London.