YouTube says it has deleted more than half of the "violent" music videos that the country's most senior police officer asked it to take down.
More than 30 clips have been removed so far.
Metropolitan Police Commissioner Cressida Dick has blamed some videos for fuelling a surge in murders and violent crime in London - and singled out drill music.
She asked YouTube to delete content which glamorises violence.
Drill originated in Chicago. Its biggest breakout star is arguably Chief Keef, famous for his 2012 track I Don't Like.
The genre's lyrics often detail vivid accounts of taking drugs and violence.
The court heard he'd penned a track about knife attacks before carrying out the killing.
Giving him a life sentence, judge Anthony Leonard QC told Simpson: "You suggested the lyrics were just for show but I do not believe that, and I suspect you were waiting for the right opportunity for an attack."
'Gestures of violence'
In the past two years police have asked YouTube to take down between 50 and 60 music videos, because they were deemed to incite violence.
The video-sharing site has now removed more than 30 of them.
"The gangs try to outrival each other with the filming and content - what looks like a music video can actually contain explicit language with gangs threatening each other," the Metropolitan Police's Mike West said.
"There are gestures of violence, with hand signals suggesting they are firing weapons and graphic descriptions of what they would do to each other.
Pressplay, a company that promotes drill music videos, said on its Instagram page that police had "forced" YouTube to take some clips down because of "what's happened lately".
But the same post said the clips "will probably be back up in the next few weeks".
A group of drill musicians called 1011 have launched an online petition to try to stop YouTube from taking down its videos.
It has more than 5,000 signatures.
A YouTube spokesman said: "We have developed policies specifically to help tackle videos related to knife crime in the UK and are continuing to work constructively with experts on this issue.
"Along with others in the UK, we share the deep concern about this issue and do not want our platform used to incite violence."