A group called Urban Fox Hunters has posted a video on the internet that appears to show a fox being clubbed to death in an east London park.
The video, which the group claims was shot in Victoria Park, appears to show the fox being drugged and chased before it is beaten with a cricket bat.
The police said they had received a number of complaints about the video.
The group said it was "performing a public service" to "keep our streets safe."
The Metropolitan Police's wildlife crime group said it had received a number of complaints which were being looked into by the local Tower Hamlets force.
Urban Fox Hunters claims on its blog to be a group of local residents who "hate foxes" and "are now doing something about it".
Its video has been removed from YouTube but is still available on the group's blog.
Writing on the blog, one member, who calls himself Lone Horseman, claimed they drugged the foxes before killing them.
He added: "We are performing a public service, which is a bit unpleasant, but it has to be done to keep our streets safe.
"I have kids and I don't want them being bitten by a diseased vermin scum, what's wrong with that?"
The RSPCA said it was investigating the video to try to determine if it was genuine.
A spokesman for animal welfare group League Against Cruel Sports said: "If the video's true then we're horrified people are behaving in this way."
"There has been over-reaction to the apparent fox attacks because they're so uncommon.
"The public in Tower Hamlets are more at risk from the idiots who wielded cricket bats and produced this than foxes."
Two baby twins were attacked by a fox at their home in Hackney, east London, on 5 June.
Last month, their mother Pauline Koupparis said nine-month-old Isabella and Lola were recovering "really well" and had returned home from hospital.