Ian Airlie, 48, was found dead in his Greenwich home on Thursday, October 10.
His family informed the police that he had been reportedly pushed down the Jubilee Line escalator at Waterloo Station at 5.05pm on Sunday, September 15.
Following the fall, Mr Airlie is believed to have spoken to station security.
He claimed he had fallen into a woman of South Asian appearance, who also fell on the escalator.
After leaving the tube, Mr Airlie reportedly spoke to a woman on a bus from North Greenwich underground station.
She handed him a tissue as he was bleeding from above his left eye.
The police are appealing to these individuals, as well as anyone else who witnessed the incident, to come forward.
Detective Inspector Chris Rogers, leading the investigation, said: “Mr Airlie’s death is tragic, and his family continue to mourn the loss of a loving son, partner, brother, and uncle.
“We are determined to piece together the events, and give Mr Airlie’s family the answers they are searching for.
“You can assist us by coming forward with any information.
“However small it may seem to you, this could be the key we need to unlock the investigation.”
At the time of the incident, Mr Airlie was wearing a black T-shirt and light grey jogging bottoms.
He had a turquoise and grey Mountain Warehouse rucksack on his back and was carrying a medium, black suitcase.
A post-mortem examination on Tuesday, October 29, was inconclusive, and further tests are awaited.
Anyone with information is asked to contact the police via 101, or anonymously through the independent charity Crimestoppers on 0800 555 1111, quoting 01/942310/24.
