Police say they are investigating and making enquiries relating the incident to site managers following the release of a free-running video shot in South London.
In the video, a group of free-runners can be seen climbing up a crane on a construction site between Shotfield and Holmwood Gardens, in Wallington.
The video was posted on 16 February to YouTube by user Neil LeightonPK. The video is accompanied by a short description which says: "We went on a crane mission early hours of today and climbed up the 50 meter [sic] crane in the old court house area of Wallington."
In the two-minute long clip, viewers are shown the climb up the 50-metre tall machine, and then follow the free-runners as they walk along the top of the structure. Seemingly unfazed by the experience, one of the young men smokes a cigarette, with a shot of London's dawn in the background.
On Wednesday night, Sutton Metropolitan Police Service (MPS) posted to Twitter saying: "Following footage brought to our attention, thrill-seeking free running will not be tolerated and offenders will be dealt with robustly."
The Metropolitan Police told The Independent on Thursday: "Police are looking at the film clip to see whether any offences have been committed.
"Local safer neighbourhoods officers have visited the site to see what steps can be taken by the site management to tighten security and prevent access to the site. If there are any offences, then the offenders will be dealt with robustly."
Watch the video of the 50-metre climb
Watch other videos from the group here.