Dickens set many of his novels around Covent Garden. I'm fairly sure that the "Who Will Buy?" scene in 'Oliver!' is based upon the hawkers who traded around the old market there (but I'm less certain about whether Dickens actually specified the location in 'Oliver Twist').
This site doesn't give a definitive answer to your question, but it does confirm Dickens' fondness for the area and also that he included it in several of his works. It also mentions that the Artful Dodger's court appearance was at Bow Street; this would seem to confirm the area of London where Oliver Twist was set:
http://www.london-walks.co.uk/46/a-covent-gard en-walk-with.shtml
Chris