We can guess this location partly because Scrooge is a trader, merchant or businessman of some sort, but also because Dickens mentions several parts of the City by name. St Paul's Cathedral, with its famous dome, is mentioned in Stave I, and on his way home to Camden Town, Bob Cratchit (we only know him as Scrooge's anonymous clerk at this stage) slides down Cornhill (a City street) on the ice. As Camden Town is several miles northwest of the City, Scrooge's offices would certainly be somewhere east or south of Cornhill.
Describing the immediate vicinity of the office (or warehouse), Dickens mentions a courtyard and "the ancient tower of a church, whose gruff old bell was always peeping slyly down at Scrooge out of a Gothic window in the wall." The church may well be St Michael's, Cornhill, on which basis the City of London's Dickens Walk identifies the exact site of Scrooge & Marley's as Newman's Court.
To see just how far Bob Cratchit would have run home from work (ran, and after 20 slides down Cornhill, no less), see this map of London from 1844. Cornhill is at roughly J5, where Camden Town is just to the right of the large green area (Regents Park) at E2, approximately.
Photo: John Salmon (licensed for reuse under Creative Commons)