In a separate incident, another device held by TfL in lost property caught fire in October.
The new rule comes into place on Monday and does not apply to e-bikes or mobility scooters.
Sarah Gayton from the National Federation of the Blind of the UK doesn’t think escooters are safe for anyone.
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.”