Beck's map of 1949 shows the Central line open to Loughton together with the Hainalt loop. Loughton-Ongar is still "Under construction". On the 1951/52 maps there is the shuttle service from Epping to Ongar. This continues through subsequent published maps, including those prepared by Paul Garbutt, until the Epping-Ongar section closed in September 1994.
Information from Alan Jackson's "London's Local Railways" (2nd Ed., Capital Transport, 1999) explains that the line switched over to the tube in various stages, reaching Leytonstone in May 1947, when there were steam shuttles onwards to Ongar, cut back to Woodford and then by November 1948 to Loughton. Epping was reached by electrification in September 1949. Steam shuttles by BR using GER locos and LNER stock continued until November 1957. The line was then electrically fed from Epping and could support two 4-car units, which passed at North Weald. Finance (or lack of it) reduced the service to just the one train from October 1976. From December 1982 it was a Rush-hour only service and closure came in September 1994. Alan Jackson does not mention when the conductor rails were removed.