In the first incident, the victim and a separate group boarded the service at Slade Green station and individuals within the group started yelling at one another.
The victim asked them if they could quieten down a little before she was threatened by one member of the group who also barged into her.
The victim retreated to another carriage but was followed by the group who then started attacking her – kicking her in the head and hitting her with glass bottles.
She managed to get off the train at Erith station with other passengers who provided first aid before she was treated at hospital.
The group stayed on the London-bound train.
In the second incident, the victims, a couple, were on the train when a group of people they didn’t know started verbally abusing them.
A short while later, a girl from the group started attacking the female victim with a wine bottle before the rest of the group attacked them both.
Both victims were pulled to safety by other passengers who were also assaulted by the group. The victims got off the train at Belvedere station and the group stayed on the train.
The victims were treated for facial and head injuries at a local hospital.
Officers believe those in the images may have information which could help their investigation.
If you recognise them, or have any information, please contact BTP by texting 61016 or calling 0800 40 50 40 quoting reference 492 of 11/09/21.
Alternatively, you can contact Crimestoppers anonymously on 0800 555 111.