The students are being persuaded to take out mobile contracts, and then sell the phones on to another company. They are promised an income from the phone as well. But more often than not they end up being liable for the new user's debts.
One student ended up owing £10,000, according to police. BBC Radio 4's You and Yours programme has found the scam has affected at least a dozen universities, and police are investigating at least 350 cases where students have lost money. Typically, students take out a phone contract in their own name, and then sell the handset to a private company for £50 or so, with the promise of more money to come.
One student, who spoke to the BBC anonymously, sent off six phones and ended up with a debt of £500. "The guy from the company turned up to my Uni. He steps out of the car - and he's looking really sharp, wearing a nice suit - and he gave a really convincing sales pitch," he told the programme. "I feel a bit silly for being duped into this," he added.
Police say they are still trying to work out how widespread the scam is. They say there may well be thousands of cases which have yet to be reported. "You've got to remember these students - 18 or 19 year-olds -are probably leaving home for the first time," said detective chief inspector Bob Mahoney, of the National Mobile Phone Crime Unit.
"They've got all the worries of student debts behind them, so any income they can generate does look attractive," he said. Students are being advised not to give away personal details, and to look at their credit ratings to see if any changes have occurred.