Johnson attempted to traverse the 1,000-foot zip line while waving a pair of Union Jack flags Wednesday but ended up stuck about 65 feet from the end of the ride, The Sun reported Thursday.
"Get me a rope, get me a ladder," Johnson was heard shouting.
"I think the brakes got stuck," he said after workers were able to get him to the end of the ride.
The mayor's office joked about the incident.
"Fortunately, the mayor survived his first zip wire experience. Clearly the judges are likely to mark him down for artistic interpretation. Unlike Team GB, he won't be bagging any gold medals. But he remains unbowed," a representative said.