The announcement of a criminal inquiry came as Hennes & Mauritz, the high-street fashion chain, became the first company to sever its links with the model over the drugs allegations. H&M, which is based in Sweden, performed a U-turn after vowing last week to give Moss a "second chance" and cancelled its £2m advertising campaign featuring the Croydon-born model, saying she was no longer compatible with its anti-drugs stance.
News of the police inquiry and H&M's decision will increase pressure on the host of high-profile companies, including Chanel, Dior and Burberry, which pay Moss an estimated £4m a year to be the "face" of their brands.
The police investigation has been ordered by Assistant Commissioner Tariq Ghaffur, in charge of Specialist Operations, who is said to believe that she should receive no special exemption from the law because of her celebrity status. It is understood that the investigation will try to establish whether the model's boyfriend, the Babyshambles singer Pete Doherty, was involved in obtaining the drugs.
Moss, 31, will be interviewed under caution by officers led by Deputy Assistant Commissioner John Yates, in charge of the Metropolitan Police's anti-drugs operations.
A senior police source said: "We want to ask her who her supplier was; whether, for instance, it was her boyfriend. There is no reason why she should not be interviewed. How can we arrest working-class kids in Brixton and turn a blind eye to celebrities? It is up to Ms Moss whether she wants to talk to us. We do not know what will happen; she may just get away with a caution."
The Metropolitan Police Commissioner Sir Ian Blair has said his force will crack down on "middle-class" drug usage.
The investigation will also dent any hopes that a strategy of silence on the part of Moss and her corporate partners will allow them to ride out the storm over covert photographs published last week in the Daily Mirror.
Experts said the model's sacking by H&M could provoke a stampede by fashion multinationals anxious that Moss, who also has a deal with the make-up house Rimmel, has become a liability. One marketing executive linked to H&M told The Independent yesterday: "There has been a period of a few days where people have waited to see which way the wind is blowing on this - is Kate still a cool rock chick or is she a fading star?
"Lawyers have been consulted and brand managers have been wringing their hands. If one of the companies has decided she's more trouble than she's worth, it's likely others will reach the same conclusion."
H&M had initially stood by Moss after it said she had expressed remorse about the pictures, which show her apparently snorting cocaine during a recording session in London with Doherty. It was reported yesterday that she has since ended the relationship, causing Doherty to go on a rampage during a concert in Ibiza this week.
Representatives of H&M held a meeting with the model in New York last week, during which she was "very regretful" about the photographs. But the retailer said yesterday that it had changed its mind after "evaluating" the implications of her behaviour. The firm primarily targets the teenage and youth market.
In a statement, the company said: "H&M is strongly against drugs ... After having evaluated the situation, H&M has decided that a campaign with Kate Moss is inconsistent with H&M's clear dissociation of drugs."
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