Margaret Masson, 84, died after the Virgin train derailed on the West Coast Main Line near the village of Grayrigg.
At Lancaster Magistrates' Court yesterday, Network Rail apologised to Mrs Masson's family and indicated it would admit health and safety breaches when the case is heard next month at Preston Crown Court.
In November, an inquest jury found the train went over poorly maintained points at 92mph before plunging down an embankment injuring 88 people, including two members of the train crew.
After the hearing, Network Rail chief executive David Higgins said: "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.
"While there were faults at hand in 2007, we have been determined to recognise what we got wrong and put it right."
He added: "Since the accident, much has changed in the way we plan and carry out maintenance work, with new systems put in place to improve the quality and safety of our railway. We have one of the safest passenger railways in Europe, and safety will always be our number one priority."
A spokesman for the Office of Rail Regulation (ORR) said: "Our thoughts are with the family of Mrs Masson and all those involved in this incident. ORR will do everything it can to ensure that the prosecution proceeds as quickly as possible."
The crash occurred five years ago this month and with Mrs Masson's brother and son both in court, it took just five minutes for Network Rail to admit it was at fault. Prashant Popat QC, representing the firm, said he was authorised to enter a guilty plea.
Legal technicalities mean the plea is still an "indication" as the firm could not formally enter a guilty plea until a further hearing at Preston Crown Court.
Nicholas Hilliard QC, representing the ORR, told the court it was the failure of the stretcher bars – either detached, missing or broken – that caused the derailment, but investigations revealed "that the system for inspection and maintenance were themselves inadequate and what systems there were had not been properly followed".
He said there was inadequate training of staff, proper safety measurements between the bars were not provided or used, nuts were not tightened to the correct torque, tools to do the job were not provided and inspections were missed.
George Masson, 62, the son of Mrs Masson, left court with his mother's brother, William Devlin, 70, who had travelled from Scotland for the hearing.
Mr Masson, an engineer of Castlemilk, Glasgow, said: "I knew from day one they would be guilty. I'm relieved they have admitted it, but sad they could not apologise face to face, not just through the media.
"My heart has deteriorated so much since all this, the stress and anxiety. Tears welled up when I was sat in court, just the mention of my mum. I'm happy this will come to an end now, it's took five long years.
"Network Rail have never learnt their lesson; there was another derailment a couple of weeks ago at a rail crossing, someone was killed."
Last month, senior management of Network Rail, a firm backed by a taxpayer guarantee, decided to forgo six-figure performance bonuses after coming under political pressure.
Chief executive of Network Rail, Sir David Higgins, in line for a possible £340,000 bonus on top of his £560,000 salary, announced that directors' bonuses would instead be allocated to improve safety.
Mr Masson added: "I think it was a hollow gesture on their part, refusing the bonus. They don't deserve it."