The report classified the incident at Baildon near Bradford as a "near-miss"
Three trains passed over a dangerous piece of track over an embankment which had been washed away, a report says.
The incidents happened at Baildon, near Bradford, last June, when floodwater washed away part of the embankment leaving a rail unsupported.
Although no trains were derailed and no-one injured, the Rail Accident Investigation Branch (RAIB), external classes what happened as a "near-miss".
Network Rail has been told to improve its safety procedures.
The RAIB report said members of the public reported the problem but it was not acted on quickly enough.
The report said two members of the public contacted the emergency services saying that between 3m and 4m of track was left unsupported following a rainstorm.
Both the police and fire service passed the calls on to Network Rail.
'Minimise the risk'
Two trains passed over the damaged area between 16:29 and 17:58 GMT on 7 June.
Services were finally stopped when a driver spotted the washout as his train passed over it and made an emergency call to a signaller.
The RAIB recommended Network Rail should take "measures to minimise the risk of further washouts at Baildon" and take action on "improving the emergency response to incidents on the track by providing Network Rail responders with accurate location information".
A spokesperson for Network Rail said: "We have worked closely with the RAIB on this investigation. Safety is our top priority and we have one of the safest railways in Europe.
"We were already making changes which are covered by the RAIB recommendations and are implementing a new training programme to help prevent an incident like this happening again."
