It's possible that different colleges have different views on this, but on the Downing College interview prep webinar on Thursday, this came up in the question and answer section at the end. The response was that it's perfectly fine to have a copy of your personal statement and any work you've submitted to the college in front of you during the interview. Blank paper for making notes was also recommended.
The admissions tutor implied that having other reference material near you was fine too, but that wasn't terribly clear. (For English, I'm not sure what reference material would be useful anyway.)