The woman, aged 20, arrived in the Italian city to take part in a photo shoot but was abducted and held for five days.
A polish national who lives in the UK has been arrested on kidnapping charges.
The Foreign Office said it was providing support to a British woman.
Police said the woman was drugged, handcuffed and put into a bag and then into the boot of a car.
The car was then driven to an isolated house in Turin.
The woman was then kept handcuffed to a wooden chest of drawers in a bedroom for six days until she was released.
The kidnapper used an encrypted account and then asked the model's agent for $300,000 to stop her from being sold in auction.
He said he was working for The Black Death Group.
The kidnapper was captured by police while he was accompanying the model to the British Consulate in Milan.