The man launched himself down the 196ft (60m) escalator at Angel Tube station and filmed the stunt.
The unidentified man then posted it on the YouTube video sharing website where it has received more than 100,000 hits.
Transport for London (TfL) urged police to take the "strongest possible action" against any similar offenders.
'Reckless' stunt
A TfL spokesman said: "This is a dangerous, stupid and irresponsible act that could have resulted in serious injury or death to not only the individual concerned, but other passengers."
