Confirmation of the investigation came a day after Hennes & Mauritz, Europe's largest fashion retailer, canceled plans to use the 31-year-old model in an upcoming ad campaign.
The decision to drop the campaign came after Moss acknowledged last week that British tabloid reports of her recent cocaine use were true.
H&M initially said it would proceed with the campaign, but company spokeswoman Liz Asarnoj said Tuesday that "after evaluating the situation, we have decided that a campaign with Kate Moss is not consistent with H&M's clear disassociation with drugs."
Chanel, the French fashion house, said Wednesday it wouldn't renew Moss' contract when it expires next month. "The contract was always going to end in October," said Julie Le Blevec, spokeswoman for Chanel perfumes.
Moss has been the face of Chanel's Coco Mademoiselle perfume since 2002.
Burberry also said it was canceling a planned campaign involving Moss.
London's police generally investigate drug dealers rather than users, but that policy is "adaptable to the impact of events," said Ian Blair, commissioner of the Metropolitan Police.
Blair told reporters he wouldn't comment directly, but added: "We have to look at the impact of this kind of behavior on impressionable young people and if there is evidence, something should be done about it.
"I can remember being asked a question about a previous individual who was given a caution. I think that was a wrong decision."