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The unidentified mother was filmed holding her toddler son on her lap while abusing black passengers.
The expletive-filled video shows the white mother on a tram screaming abuse at passengers on the Croydon to Wimbledon service in South London.
The brunette mother blasts black, Polish and foreign commuters with a hate-filled tirade demanding they "go back to their own country", saying that they are not British.
The footage has been viewed thousands of times by internet users - with many reacting angrily and calling for the woman to be arrested and charged.
A fellow passenger filmed the woman - whose blonde-haired son is seen sitting on her lap playing with an action figure - for around two minutes as her rant continued.
During the footage the mother - who at times appears to slur her words - begins by ranting and directing her comments at several passengers.
She starts: "What has this country come to?...with loads of black people and a load of ----ing Polish.
"You ain't English eeva (sic), none of you are ----ing English, get back to you're own ----ing, d'you know what?
"Sort out your own countries, don't come and do mine, Britain is nothing now, Britain is ---- all, my Britain is ---- all now."
As the rant continues with the woman seemingly not caring about her swearing even in front of her young son, one brave passenger intervenes.
The passenger - which the camera pans to reveal is black - said: "Excuse me dear, there's a lot of kids on the tram."
The woman then replies: "Yeah fine, I've got my little kid here."
The passenger then tells the woman she should have some respect and picks her up on her swearing in front of the children.
She said: "There are little boys here who don't use those words"
The mother again says she has her little boy with her to which the passenger replies: "well get off the train then."
The mother then begins swearing again telling the passenger to ---- off and that she ----ing dares anyone to throw her off.
Despite the passenger trying to calm the woman down by telling her again to watch her language it only seems to add more fire to the racist rant.
The mother continues: "Go back to where you come from" and then appears to try to say the name of the country 'Nicaragua' but beginning with 'n-----'.
At this moment a young black male sitting behind the mother and her son jumps to his feet seemingly annoyed by the use of the offensive term but he is quickly told to calm down by others on the tram.
The passenger challenging the mother says to the woman: "If we didn't come here you guys wouldn't have people to work.
"We have to come here and do the work for you."
The mother claims she has a job and does work.
The mayhem continued with the mother telling the passenger who had told her not to swear that "she is not British" to which the passenger responds firmly "I am British".
Finally as the scene becomes increasing heated a white passenger, who says she is English, tells the mother to stop.
She said: "Now you're ----ing waking my baby up so do you want to shut your mouth?
"I'm English, what have you got to say to me, ---- all, so shut your mouth."
The video was uploaded to YouTube by user ladyk89, labelling it "My Tram Experience", where she says the video shows a "British woman on London transport complaining that Britain is nothing now that ethnic minorities are in her country".
A British Transport Police spokesman said: "The video posted on YouTube and Twitter has been brought to our attention and our officers have launched an investigation.
"At present it is not entirely clear which tram stops the offence took place between and when it occurred. As a result we need anyone who witnessed this incident, or with any information that could assist our investigation - including the identity of the woman - to contact us.
"We will not tolerate racism in any form on the rail network and will do everything in our power to locate the person responsible."