For Bristol, I had an on-paper interview, where they sent me a list of 15 questions and I had to fill out the answers.
For Roehampton, I had an hour-long phone interview. It was me, the Dean of the graduate college, the head of the department, and four professors who were potentially interested in being my advisor. I was pretty well grilled about every answer I had put on my initial application. I was asked to say something about the paper I'd been presenting. I was asked about my career change. I was asked about my theoretical approaches and background. I was asked what shows I wanted to work on for my thesis. I was asked what research experience I had.
It wasn't a stressful thing, though, by any means. I'd approached the department before my application, so I knew they were interested in my research. The interview was somewhere between a formality and an opportunity for the professors to decide who would lead my advisory committee.
The way the admissions process goes, in general, is that you send the application to the university admissions department. They look it over and see if you meet the university's admissions standards (do you have the prerequisite degree? have you filled out the application completely? do you have your transcripts and recommendations?), then pass it on to the department for the real decision.
The best thing to do is, as a few of us have mentioned, look into who is doing what in your field. Then send off some s-mails to those departments, introducing yourself and explaining your interests. If they have a stack of applications, they're going to be more favorable to the one from the person they've corresponded with, who isn't an anonymous entity.