The incident took place between Dunbar and Edinburgh in the early hours.
Replacement buses have been in operation, calling at Berwick and Alnmouth for Alnwick.
LNER reports that lines have reopened between Dunbar / North Berwick and Edinburgh as the emergency services are now clear of the line.
However, it warns that trains may continue to be cancelled, delayed or revised and that disruption is expected until 12pm.