@Kimberley Back in my day, one didn't seem to have to apply for a PhD place, I was just told that one was open to me (in the same institution where I was finishing my first degree), with X as supervisor.
Then I was chatting to Y, another academic in the department. "Y'know, X's students don't usually end up with a PhD" he said.
I was too politically naïve to understand what he was saying, and did nothing in response. I started the PhD course with X as supervisor and dropped out after a year.
I realised some considerable time later that what Y was suggesting was that I should request a change of supervisor, presumably that Y should be my supervisor instead. But he couldn't say that explicitly - it would be unethical to poach someone else's student - it would have to look like my idea.
So, to answer your question, I should have asked "can I have Y as my supervisor?"