I don't think we're meant to be able to identify specific individuals and I'm not sure that Duffy wants us to do that. Her concern in the poem is to explore the relationship that a biographer has with his subject, after all, the title puts the focus on the writer, not the subject. The content seems to focus on those biographers who become completely enveloped or obsessed by their subject that they want to explore every facet of the individuals life. In this case the person would seem to be a Victorian writer, possibly a composite character. Richard Ellman's biography of Oscar Wilde has been suggested as the type of work Duffy is alluding to.