Whom should I approach in the Physics Department to act as a referee for a job or internship application?
If you need a personal reference then please ask your college mentor or Senior Tutor. For an academic referee it is normal to use your physics academic adviser. If your adviser is unavailable, or if you need a second academic referee, then you could ask your current or previous Level 1 physics tutor, or (for Level 4 students) your Project Supervisor. If you are a Natural Scientist then you may approach the Physics Department's Natural Sciences Liaison Officer (see http://www.dur.ac.uk/physics/students/natsci/) to act as second academic referee. The Director of the Natural Sciences programme is also able to provide a general (not subject-specific) academic reference.
If you are taking a module with significant laboratory component (such as the Level 3 Laboratory Project, Team Project or Computing Project) then you may consider asking your Laboratory Supervisor to act as second academic referee.
Note that if you nominate someone as your referee, then that counts as giving consent to their disclosing information about you to the relevant company or organisation. However, your referees will not normally disclose sensitive personal data (such as relevant medical information) without first obtaining your explicit consent.