Margaret Masson, 84, from Glasgow, died from multiple injuries after a Virgin Pendolino London to Glasgow express train crashed on the West Coast Main Line near the village of Grayrigg on February 23 2007.
The 300-tonne locomotive derailed at 95mph after hitting a faulty set of points, with all nine carriages of the Class 390 tilting train coming off the tracks.
A further 86 passengers and two crew were injured, 28 seriously.
The firm's lawyers appeared at Lancaster Magistrates' Court for breaching health and safety law, following criminal proceedings started by the Office of Rail Regulation (ORR).
Network Rail, which is responsible for track maintenance, is facing a charge under section 3(1) of the 1974 Health and Safety at Work Act.
Stretcher bars holding the moveable rails a set distance apart when the points are operated failed, causing the train to derail.
Network Rail chief executive David Higgins said later: "The Grayrigg derailment in 2007, resulting in the tragic death of Mrs Masson, was a terrible event."
"Within hours of the event it was clear that we were responsible, that the infrastructure was at fault, so it is right that we plead guilty. We again apologise to Mrs Masson's family for the undoubted grief this has caused them."