The Crown Prosecution Service, which in 2022 authorised two charges of indecent assault against Weinstein, on Thursday said it decided to discontinue proceedings because there was "no longer a realistic prospect of conviction".
"We have explained our decision to all parties,'' the CPS said in a statement.
''We would always encourage any potential victims of sexual assault to come forward and report to police, and we will prosecute wherever our legal test is met."
Meanwhile, there is a chance Weinstein could be facing new criminal charges in New York.
At a court conference on Tuesday, Manhattan prosecutors said they have begun presenting evidence to a grand jury to seek an indictment that could add sexual misconduct allegations involving as many as three more people who say they were victimised by the producer.
At the conference, Judge Curtis Farber elicited basic details about the allegations, which date back as far as the mid-2000s and involved incidents at hotels and a private residence.
The New York grand jury's term expires on Friday, and a vote on an indictment could happen by the end of the week. It is possible an indictment may not include all three accusers. And it is possible the process could extend beyond this week.
Weinstein became the most prominent villain of the #MeToo movement in 2017 when women began to go public with accounts of his behaviour. After the revelations emerged, British police said they were investigating multiple allegations of sexual assault that reportedly took place between the 1980s and 2015.
In June 2022, the Crown Prosecution Service said it had authorised London's Metropolitan Police Service to file two charges of indecent assault against Weinstein in relation to an alleged incident that occurred in London in 1996. The victim was in her 50s at the time of the announcement.
Unlike many other countries, Britain does not have a statute of limitations for rape or sexual assault.
Weinstein has denied that he raped or sexually assaulted anyone.
In 2020, he was convicted of rape and sexual assault in New York. But a new trial was ordered after the state's top court ruled that the judge in the original trial unfairly allowed testimony against Weinstein based on allegations that weren't part of the case.
Weinstein remains in custody in New York while awaiting retrial in Manhattan.
After the retrial, he is due to start serving a 16-year sentence in California for a separate rape conviction in Los Angeles, authorities said. Weinstein was convicted in Los Angeles in 2022.
Weinstein, the co-founder of the Miramax entertainment company and The Weinstein Company film studio, was once one of the most powerful people in Hollywood, having produced films such as Pulp Fiction and The Crying Game.
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