Before the War you, working with your partner Dr Watson, were a celebrated and successful detective, using your systematic and logical powers of deduction to produce almost superhuman conclusions.
Both you and Watson remained in London, resisting the panic that seized most of the population and helping to organize some few of the refugees to a more successful escape, drop in the ocean though your efforts were.
Finally, even you were driven out and Watson was killed; you bear a burning hatred for the Martians as a result. Added to this is the personal affront of their inhuman nature; as a supreme expert on human psychology and motivation, their obscure and inexplicable thoughts and motivations infuriate you for being impossible to understand.
Within London you have many contacts and associates, including a gang of street toughs led by a guttersnipe named Davy McCann, and one Inspector Lestrade of Scotland Yard who owes you a favour or two.
You at times border on arrogance, and draw pleasure from baffling police inspectors with your superior deductions. You do not seek fame, however, and are usually content to allow the police to take public credit for your work.
You occasionally use addictive drugs, especially when lacking stimulating cases. You are a habitual user of cocaine, which you inject in a seven-per-cent solution using a syringe kept in a Morocco leather case. You are also an occasional user of morphine, but express strong disapproval of opium. These drugs are legal in late 19th-century England. You have iron self-control of these habits, but even so, you remain an addict whose habit is "not dead, but merely sleeping", and withdrawal can make you erratic.
(There doesn’t have to be any more Benedict Cumberbatch in this character than you want there to be…)