PhDs in the UK: should you know supervisor beforehand?
It is not necessary to know a professor before applying for a PhD in the UK. I have so far supervised 8 PhD students, only one of whom I knew before they started their PhD.
There are two routes to a PhD in the UK. First is to apply for an advertised position or program. This is how the majority of PhDs are recruited, but it is also usually only open to home students. The second is to find the funding yourself (either through a non-UK government scheme, an NGO or a wealthy benefactor) and to write to the supervisor laying out your experience, your desire to do a PhD (and why with them), and what your source of funding is.
I don't take unpaid interns as I feel it unfairly advantages those that can afford to do an unpaid internship at the expense of those that can't. My university runs several schemes that fund summer internships and my professional society also has a summer studentship fund. Unfortunately, I only have the capacity to take one, or at a push, two summer students a year, and I would normally recruit these from our own undergraduate body. While I try to reply to all requests for internships, I get several a day during some parts of the year, and sometimes they slip through the cracks.