It emerged that Miss Banks had earlier been seen at Tunbridge Wells Hospital but was sent away as she was not in labour and contractions had not started.
Commuter Neil Perkins, 22, a recruitment consultant from Maidstone, was sitting close to Miss Banks before she went into labour. He said his "jaw dropped" when he realised she had given birth.
A man claiming to be the uncle of baby Phoebe, who was born on a commuter train from London Victoria to Kent yesterday evening, has tweeted to say his niece is "well and safe."
No trains are running into or out of London Victoria train station due to a train fire.