Activists have demanded an “instant ban” on the electric vehicles being allowed on the London Underground.
The shocking video shows a man coughing badly following the scooter fire.
A Transport for London (TfL) spokesperson said a urgent full safety review was underway, while Andy Lord, managing director of London Underground, said that an announcement will be made very soon.
Disability advocates from the National Federation of the Blind of the UK (NFBUK) have called for all private e-scooters to be banned from TfL services immediately.
In a statement, a charity spokesperson said: “The film showing the smoke filling the train and the fire from the e-scooter was frightening and terrifying.
“We cannot understand why there was not an instant ban on them being allowed on TfL services and call for immediate action to be taken to prevent further risk to human life.”
Sarah Gayton, a street access campaign coordinator with NFBUK, said: “It’s been a month since the e-scooter fire at Stanmore and just under four weeks since the e-scooter fire at Parsons Green Station and TfL is carrying on as nothing has happened.
“It is absolute insanity to allow passengers to take private e-scooters onto the underground and on any of the services.
“These e-scooters are an immediate fire risk and they need to be off all TfL services.”
Ms Gayton, who has been calling for e-scooters to be removed from the network since the trial began in June this year, added: “Imagine being squashed together on the underground when one of these machines starts to smoke and then bursts into flames.
“There would be absolute panic and people would get killed, they would be burnt alive, choked to death from the smoke or suffocated to death through the crush.
“It is that simple and there should have been a ban introduced instantly after these fires happened.
“We call upon Andy Byford to take immediate action and to ban them.”
Speaking to LondonWorld, Ms Gayton added: “It is utter madness that TfL senior leadership do not grasp the severity of risk to human life by allowing e-scooters onto their services.
“Especially underground, where there is absolutely no escape from the smoke and flames if these go up. It‘s already happened and they were lucky it was on an outside platform.
“It is beyond complacency and incompetence and serious questions need to be asked why they are still being allowed on their services.”
Lorraine Ward, organising director at the Transport Salaried Staffs’ Association (TSSA) said: “Without doubt the incident at Parsons Green raises very serious concerns. It’s becoming all too clear that e-scooters pose a significant threat to the traveling public, our members and all workers at TfL.
“There should be an immediate halt to transporting them on all TfL services until more research into these batteries has been carried out.
“I’m therefore urging TfL to fully enforce the already existing ban on the use of e-scooters. A further ban across the wider travel network should be considered by the Secretary of State for Transport.
“What happened at Parsons Green and recently at Stanmore must be properly investigated as soon as possible.
“Safety on our transport network will always be our union’s number one priority, there can be no compromises on that.”
A TfL spokesperson said: “We completely understand how worrying it was for our customers and staff during the incident when an e-scooter caught alight on a train.
“While incidents like this are very rare, we take safety on the network extremely seriously and are urgently undertaking a full review of our bye-laws, which includes liaising with the London Fire Brigade.”