The Student Loans Company took more than £15 million in overpayments last year from graduates who had already paid back all the money they borrowed.
More than 57,000 former students were waiting for a refund for the year to March 2010, according to Which?.
The consumer watchdog obtained the figures using Freedom of Information requests after receiving complaints from people who noticed money was still being taken from their pay packets despite the fact they had already paid back their student loans in full.
Under the loan system, graduates pay back the debt in monthly instalments docked from their salary.
HM Revenue and Customs takes the money and passes it to the SLC until the SLC informs HMRC the total has been paid.
Although the overpayments are eventually repaid, Which? said graduates faced "hardship" and "hassle" as a result of the situation.
The SLC told Which?: "If a borrower has overpaid, the money is paid back when the details come to us. Borrowers suffer no financial disadvantage as a consequence."
Which? principal advocate Mark McLaren said: "We disagree. Unwarranted payments could cause significant short-term hardship, as well as considerable hassle in getting HMRC and the SLC to communicate effectively with each other."
The figures emerged a week after MPs criticised the SLC - the Government agency set up to deliver grants and loans to students.
The House of Commons Public Accounts Committee (PAC) described the performance of the SLC as "completely unacceptable" in its first year and said improvement since then had been "disappointing".