As far as I'm aware, the goods yards on the former 'big railway' stations at the east end of the Central Line closed in the late 60s.
There were also a couple of Liverpool Street - Epping passenger trains early Sunday mornings in to the 60s (again, not sure when they ended - I have a 1961 underground timetable that shows them calling at Stratford (presume must have been ER platforms not the central line platforms), Leyton then all stations.
I can find an article "freight on the underground" on the
LURS website (opens as PDF) which has more on freight workings to the Central line (and others)
1950-ish OS maps show a north/eastbound link to / from ER tracks just west of Leyton Station
here (now under the A12) and a south/westbound link just before the central line goes in to tunnel
here