She was allegedly assaulted and drugged when she arrived at the studio the next day, then placed in a vehicle boot and taken to a small village near Turin where she was kept prisoner by Lukasz Pawel Herba, a British resident born in Poland, police said.
Reports also suggest she had the drug Ketamine injected into her arm, reports Corriere della Sera.
In a letter sent to the victim upon her release, Black Death told her that a "mistake" had been made in capturing her.
They said she was handcuffed to a dresser until she was released near the British consulate on 17 July - with the suspect arrested the day after.
The kidnapper was captured by police while he was accompanying the model to the British Consulate in Milan.
Italian police say the offender demanded 50,000 Euros to free her and "threatened to kill her" if she told officers what happened to her.
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According to court documents, the woman was drugged by her abductor and held in a small town in the north-western Piedmont region of Italy.
Prosecutors described the kidnapping as a "very well-organised seizure" and added he was contacted over the internet two days later with requests to "buy" her for sexual purposes.
The man has confessed to the crime and his phone and computer - including photos of the model being offered on the "deep web" - have been confiscated.
While it is unclear why the kidnapping came to an end, it is the reported the 20-year-old was released because she had a two-year-old child and the gang's "rules" prevent them from kidnapping and trafficking mothers.
Italian police said they are working with officials in Britain and Poland as they continue to investigate.
The British Foreign Office said only that it is providing consular support to a British woman in Milan and that it is in touch with local authorities.
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