Part-Time PhD in the UK? How does this work?
Full-time PhD student here (my office mate is part-time).

As you say, many universities will have a part-time program. It probably is possible to work full-time and do research part time, but it will be even more challenging than usual. PhDs tend to work best if you immerse yourself fully and spend your energy exclusively on research (especially if you want to have some spare time).  My friend finds it difficult to balance a 20 hour workweek and a part-time research position. I've never met anyone who has a full-time job on top of the PhD.

Re funding: AFAIK grants are typically used for full-time studentships. In my group, we have often broken down a full-time position into two part-time ones, but only for postdoctoral researchers. I guess the assumption is at a postdoc level people will be better at juggling all their commitments. My supervisor won't admit to it, but I reckon he would prefer one full-time student as opposed to two part-time ones, as the former is more likely to complete.

EDIT: I spoke to my supervisor. If your day job is related to the research and is likely to help you (as opposed to holding you back), he said he would consider it a plus.