In BrE, we would say that you study at + name of university. In addition, we don't usually put "the" before the name of the university unless the name uses the form "The University of East Anglia". For institutions such as Oxford University, Leeds University, Manchester University, etc, no article is needed.
I am studying biology at Manchester University.
I am an undergraduate at Leeds University.
I am studying politics at The University of East Anglia.