Nathaniel Armstrong, 29, was killed in Fulham, west London, just days after the presenter made an impassioned on-air speech about knife crime.
Lovel Bailey, also 29, was alleged to have stabbed the victim during an argument in the early hours of Saturday 16 March.
He was subsequently arrested at Gatwick Airport.
The defendant of Bromwich Walk, Little Bromwich, Birmingham, was due to face trial at the Old Bailey in November but at a hearing before Judge Wendy Joseph QC, the prosecution announced it was not continuing the case.
Oliver Glasgow QC said the “strength of the evidence” against Mr Bailey meant there was no realistic prospect of conviction.
Mr Bailey had already been released from custody and the family of the dead man informed, he said.
Judge Joseph made clear to discontinue a case was not the same as a not guilty verdict, adding: “The crown are saying they do not even have a case to bring at the moment.”
Mr Beresford, 38, had described his cousin as “a bright young man with his whole future ahead of him”.
The killing happened 11 days after the the Good Morning Britain weatherman spoke out about knife crime on the ITV breakfast programme.
Mr Armstrong died in Gowan Avenue – the same street where TV presenter Jill Dando was murdered 20 years ago.