If you have a look at your map (starting at Rainham) the old A2 essentially follows the existing route to Rochester and over the river bridge. The road then goes out to J1 of the M2 and at this point the original route is lost as it is all buried beneath the dual c'way. The A2 is what was Watling Street and this is still shown on most A-Z's. It reappears as a slip road just south of Swanscombe, for a short period is the B2200, before becoming the A226 through Dartford (although the original road is now pedestrianised).The A226 becomes the A207 near Crayford and continues in more or less a straight line (being an ex Roman Road), past Bexleyheath, up and over Shooters Hill (which used to be a good spot to be robbed by highwaymen, but probably not in the 50's!). When you get to the A102(M) junction, the road becomes the A2 again. It then goes over Blackheath, down the hill into Deptford and heads for New Cross. Follow New Cross Road into Old Kent Road (still on the A2, but only on the original line if coastbound due to the New Cross one way system), up to the Bricklayers Arms interchange (where the original route is lost under the 'new' flyover/ r'about) into New Kent Road (A201) and arrive at the Elephant.