In a statement, the family said there was “no evidence placing him on Putney Bridge at that time, and no credible evidence that he was the man shown in the footage”.
“In fact, the evidence proved the opposite.”
Brandram was arrested in June this year on suspicion of attempted grievous bodily harm. Last week, the Met confirmed he had been released under investigation.
The banker was found dead in his home on Tuesday evening. The force said his death was being treated as “unexpected, but is not believed to be suspicious”.
The family said that police “chose to arrest Nick rather than invite him to attend for interview”.
“They searched his home, and the Met Police press team then released information which inevitably led to speculation and Nick being identified in subsequent reporting,” they said.
“For Nick, the consequences did not disappear. He was left for months carrying the stigma of an appalling allegation which the police themselves clearly recognised was unsupported by the evidence.
“He lived with the shame, anxiety, humiliation, and extraordinary pressure created by a wholly unnecessary investigation.”
They said the police were repeatedly asked to end their investigation and warned about the impact the investigation was having on Brandram’s mental health, saying: “Even then, the investigation was not brought to an end. As a result, Nick is dead.”
