Detectives have finished their initial inquiry into "proxy" donations to Labour and have passed their findings to the Crown Prosecution Service.
A decision will now be taken as to whether there is sufficient evidence to charge anyone over the donations, which totalled nearly £664,000.
Property developer David Abrahams gave the cash to the party in the names of other people, breaking electoral law.
Mr Abrahams has said he did not know he was doing anything wrong.
The rules state than donors must use their own names when giving more than £5,000 to political parties.
Gordon Brown promised the money would be repaid and insisted he knew nothing about the arrangement involving Mr Abrahams.
The affair led to the resignation of Labour's general secretary at the time, Peter Watt, who said he had known the money belonged to Mr Abrahams but was not aware that rules had been broken.
Mr Abrahams had long given money to Labour and to charities but said he did not want the publicity associated with being a major political donor.
The Metropolitan Police have been investigating the donations since the end of last year. No arrests have been made.
Detectives have spent the past seven months working on the case
A police spokesman said: "We have had regular consultation with the CPS since the inquiry began on November 30 2007.
"It is now a matter for the CPS to consider the evidence, advise us on whether any further inquiries are necessary and whether any charges should be brought."
The Labour Party said it "has and will continue to cooperate fully with the police investigation into the matters referred to them by the Electoral Commission".
"We will not be providing a running commentary on these issues whilst the investigation is ongoing," a spokesman added.