An "urgent investigation" is under way after a university sent personal details about one of its staff to about 300 students.
The data breach on Sunday at the University of East Anglia in Norwich follows a similar episode there in June.
The university's students' union said it would be "demanding action at the highest levels".
The university has apologised "unreservedly" for the mistake.
The latest incident involved an email being mistakenly sent to hundreds of postgraduate research students in social sciences.
Exactly what personal details were shared is unclear.
A university spokeswoman said: "This was unintentional and clearly should not have happened, and the university apologises unreservedly.
"Steps were taken to immediately recall the message, and the university contacted the member of staff to apologise and offer support.
"An urgent investigation into how this happened is under way and we will make any changes necessary to the new data protection systems and training currently being rolled out to prevent incidents like this happening in the future."
The Information Commissioner's Office, which did not take action against the university after the previous breach, said it was aware of the latest error and "will be looking into the details".
Jack Robinson, campaigns officer at the students' union, said: "Given the earlier revelations about data breaches of this nature last year, this latest incident is breathtaking and we'd be forgiven for not trusting what are starting to look like hollow reassurances.
"Students are rightly questioning whether their personal data is safe in UEA's hands and we'll be demanding action at the highest levels in coming days"