Prosecutors are considering whether to bring charges against five people as part of an inquiry into alleged anti-Semitism within the Labour Party.
Met Police chief Dame Cressida Dick told LBC radio the files had been given to prosecutors last September.
It follows a police investigation prompted by an internal party document disclosed by the station in late 2018.
Labour has previously welcomed the police inquiry and said it is committed to challenging anti-Semitism.
The Met confirmed that four people had been arrested last year as part of its investigation, with a further two interviewed under caution.
The probe came after LBC disclosed a Labour dossier in September 2018 detailing messages on social media allegedly posted by party members.
Dame Cressida said it would now be up to the Crown Prosecution Service to review the evidence and decide whether to bring charges.
She added: "It is a very complex crime type, to be honest.
"There is a lot for them to look at and a lot for them to consider as to whether there is either sufficient evidence to charge."
EHRC probe ongoing
The party's handling of anti-Semitism allegations has been under investigation by the Equality and Human Rights Commission (EHRC) since May last year.
The rights watchdog is assessing whether the party has "unlawfully discriminated against, harassed or victimised people because they are Jewish".
The party has been plagued by accusations of anti-Semitism since mid-2016 - and the leadership has been accused of tolerating a culture of anti-Jewish prejudice by a number of its own MPs, some of whom have quit the party in protest.
Leader Jeremy Corbyn has insisted he is getting to grips with the issue and the party's internal disciplinary procedures have been beefed up.