There are three possible answers to your question.
The SCONUL Access Scheme allows staff & students from participating universities to access to each others' buildings. Additionally, university staff and postgraduate, part time or distance learning students are usually granted borrowing privileges. Undergraduates, however, are not.
For more information on the SCONUL Access Scheme and how to apply please visit this page
The second answer is that our Inter Library Loan service may be able to obtain books on your behalf from other university libraries. Go here for further details.
Finally, anyone who works, studies or lives in Newcastle is entitled to join the public library. Go here for an online membership form.