The RAIB's investigation is separate from the Office of Rail Regulation and the British Transport Police.
The RAIB is an independent organisation which examines accidents and incidents on the UK's railways.
There were no casualties on the train which suffered damage but did not derail, the RAIB said.
The RAIB found the locomotive changed direction because its screw reverser moved from reverse gear to forward gear.
The RAIB said Mr MacKay may not have seen, or misinterpreted, the warning lights at the level crossing.
An engineer from the RAIB has already made initial inspections at the sites.
The Rail Accident Investigation Branch (RAIB) probe will focus on emergency doors, which some passengers said were "difficult to operate".
According to the RAIB report, the company has concluded that "it would not be reasonably practicable to upgrade the crossing".
The Rail Accident Investigation Branch (RAIB) highlighted sight as a possible cause in its report on last September's accident at Halkirk.
The Rail Accident Investigation Branch (RAIB) published a report following the incident.
Two cracks discovered on the East Coast Main Line are being investigated by independent safety experts at the Rail Accident Investigation Branch (RAIB).
The Rail Accident Investigation Branch (RAIB) launched its review of safety at the level crossing in the days following the death of Mrs Hudson.
The Rail Accident Investigation Branch (RAIB) said the guard had detached the coaches and the accident happened when one of the carriages changed direction.
The signalman was distracted by a phone call and thought the train had passed in January last year, the Rail Accident Investigation Branch (RAIB) found.
While nobody was hurt in the derailment on a Saturday lunchtime, the 43-page RAIB report states the incident could have happened elsewhere with severe consequences.
The woman was trying to board a service at Jarrow station on the Tyne and Wear Metro in April, the Rail Accident Investigation Branch (RAIB) said.
The crossing sequence should be automatically started by the approaching train, but the RAIB report said that "on this occasion the crossing closure sequence commenced earlier".
The Rail Accident Investigation Branch (RAIB) said the broken sections were part of an auger drill that had "penetrated the tunnel lining before falling on to the track".
The RAIB also strongly criticised Network Rail in the report.
The RAIB also said it appeared that Mr Mackay was not wearing spectacles to improve his distance vision as he was advised at eyesight examinations in 2006 and 2009.
However, the RAIB investigation found that the phone had not been used since August 17 that year, and had not been used by Mrs Hudson on the day she died.
The report by the Rail Accident Investigation Branch (RAIB) found engineering work on the line between Southcote Junction in Reading and Westbury meant the automatic half barrier level crossing was being controlled locally.
The RAIB said the company "did not properly understand the risk" at the site because it had not taken a record of four previous accidents - one of them fatal - into account.
However, the RAIB also said Mr MacKay may not have seen, or had misinterpreted, the warning lights at the level crossing and appeared not to have been wearing glasses to improve his distance vision.
The RAIB said it had made four recommendations to Network Rail which included assessing the need for additional engineered safety measures at level crossings, like Moreton-on-Lugg and targeted improvements to its processes for managing risk at level crossings.
The Rail Accident Investigation Branch (RAIB) report said evidence gathered so far showed the car had been held at the crossing with the barriers down, but that it was then driven round the barriers and on to the crossing.
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