Have you investigated the 1866 marriage to see whether the details fit and indeed which woman Edward Driscoll married and whether he fits what is known of your Edward?
There is also a marriage in Shoreditch, 19 Jun 1865, of a Timothy Driscoll (22) boot & shoe maker, son of Cornelius Driscoll, to a Mary Ann Hagerthy, 19, daughter of James Hagerthy. Other than the name Timothy, these details look very similar to your couple. Perhaps worth looking into, if only to eliminate.