A leading academic has claimed the jogger on Putney Bridge was "pathological" in his behaviour.
Police are continuing to appeal for information as to the identity of the man, who shoved a woman walking across the bridge out of his way on May 5.
The woman landed with her head in the path of an oncoming bus, who quickly swerved to avoid her.
In an interview with the ITV programme, Craig Jackson said his behaviour indicated a belief he was "more important" than the woman on the bridge.
Jackson, the head of the psychology department at Birmingham City University, told the broadcaster the man displayed the pedestrian equivalent of road rage, and claimed he'd been "playing a game of chicken" with the woman to see who would move out of the way.
The professor added that the incident was more to do with the man's sense of worth, rather than his mental state.
The jogger sought by police is believed to live in Fulham. He's described as a white man in his early to mid-thirties with short brown hair and eyes of the same colour.
At the time of the incident, he was wearing a grey t-shirt and dark blue shorts.
Anyone with information is urged to contact the authorities.
See the video of the incident here: