When was the original line closed, and what was it called?

It was part of the North London Railway, which ran into Broad St station
(next to Liverpool St Station, but since completely demolished and now
the site is an office complex)

http://en.wikipedia.org/wiki/North_London_Railway

"The line from Dalston Junction to Poplar was heavily damaged during the
blitz. Passenger service from Broad Street to Poplar via Victoria Park
and Bow was not reinstated at the end of the war (its official closure
was 14 May 1944). The section from Broad Street to Dalston Junction was
closed on 30 June 1986."