Officers were called to the station at about 7.40pm on Wednesday after two young men and a woman barged through the ticket gates.
The woman was asked to leave by Transport for London (TfL) staff because she had lit a cigarette.
The two men she was with then threatened a member of staff and and lunged forwards to try and attack them.
When the victim and another TfL worker quickly retreated to the staff office for their own safety, the group pried open the door.
The two men then punched the staff members multiple times.
Pc Luke Dear, from British Transport Police, said: "This was a shockingly violent and determined attack on staff who were simply trying to do their job, they should be able to do their job without the fear of an assault.
"Thankfully they weren't seriously injured but of course were left incredibly shaken by this terrifying ordeal.
"We believe the men and the woman in the CCTV images may have information which could help our investigation, and we'd like to speak with them as soon as possible.
"If you recognise them, or have any information, please contact BTP by texting 61016 or calling 0800 40 50 40, quoting reference 561 of September 18, 2019."
Vernon Everitt, managing director of London Underground, said: “This sickening attack on our colleagues at West Ham station will not be tolerated.
"We want the perpetrators brought to justice and will work with the police to do everything we can to apprehend them and then prosecute them to the fullest extent of the law.
"We call on anyone who has information on this horrific attack to get in touch with the British Transport Police.”
Alternatively, witnesses can contact Crimestoppers anonymously on 0800 555 111.
