The video - which has already received well over 120,000 views - lasts just over two minutes, and shows the woman telling several people to return to their own countries.
The video - titled "My Tram Experience" - contains explicit language and racial content that may be considered offensive. Please watch at your own discretion.
She complains that her "Britain is **** all," before a black lady intervenes and tells her to have some respect, largely because many children are on the tram.
Another British mother, whose child begins to cry, tells the woman
: "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."
A spokesman for the British Transport Police 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."
After watching the video, one user posted
: "She makes me furious." Another said: "So much hate, actually ashamed to be British."
Even CNN's Piers Morgan was disgusted
. “Very encouraged by [the] level of outrage on here to the #MyTramExperience video. Britain is so much better than that vile bigoted creature," he tweeted.