The climbers posted the footage to YouTube sparking the police operation and warnings to construction companies to secure their sites.
A police spokesman told the Sutton Guardian: “We are getting hold of a still from that video. We will work to identify them individually and work with local police teams to do that.
“We also want to have a closer look at the video to see if any offences have been committed. We would also be looking at whether their actions constitute anti-social behaviour.
“We will be working with site security, around the crane, to increase patrols and would appeal to members of the public to come forward and tell us who the individuals are.
“What they have done is tremendously dangerous and they are putting their lives at risk. We will be doing our duty to the public to protect their safety.
“This was such an incredibly dangerous and stupid thing to do that it’s almost beyond belief. They could easily have lost their lives.”
He said the teens would be dealt with ‘robustly’ and police would be talking to the Health and Safety Executive and the site’s management in Wallington about tightening security to prevent any further activities.