The incident resulted in severe burns to the 25-year-old's thigh and calls for a review into monitoring people being transported in police vehicles.
The woman had been placed in handcuffs behind her back following a report of a disturbance on Saturday, April 27.
She struggled violently with the arresting officers, making it impossible for them to search her thoroughly at the time, and the lighter she was carrying was not discovered.
On the way to London Road police station, the escorting officer chose not to sit in the rear-facing observation seats, which would have allowed him to continually monitor the woman throughout the journey.
He therefore did not see her setting fire to herself with the lighter until the flames had taken substantial hold.
An independent investigation has today recommended that Police Scotland undertakes a review of the guidance given to officers regarding monitoring people being transported in police vehicles.
An investigation report, for the Police Investigations and Review Commissioner (PIRC), found that at present the standard operating procedure allows some discretion for officers on the monitoring of people being transported in police vehicles.
Investigators for the PIRC have recommended that this be reviewed in light of this incident.
The incident was referred by Police Scotland to the PIRC on April 27, 2019. As part of their investigation, PIRC investigators examined the police van, interviewed the relevant officers and the injured party and examined the force standard operating procedures.