LikeDylan those are wise words.
I warn my Doctoral candidates that a PhD will ruin their lives - that is, it will take over. It is intense, as it should be. It needs to be tough because it is the final piece of an apprenticeship that then certifies you to go on and do independent knowledge-generating work.
You don't have reading lists or essay titles. You are alone with the blank page.
I have never really suffered deep uncertainty about my research (my insecurities are in other areas) probably because I was never the best or brightest (never came top of the class etc). I was always 2nd or 3rd. So I just worked very hard, not in a competitive way, but for the utter love of and drive to find things out. I'm 20 years on from my PhD now, and I feel I'm just coming into my intellectual maturity. It feels good!
So you really need to think about why you want to do a PhD. If you want an academic career, you'll need to be available for part-time teaching, you'll need to present your work at conferences, you'll need to be involved in your Department/School's intellectual life.
These things are hard to do part-time, or at a distance. You can do a PhD without them, but you it will take you a lot longer to get the other parts of your CV up to speed for an academic job (if that's what you want).
The universities you mention will be rather wary of taking on a self-funded part-time Doctoral candidate - well, I would be, certainly (not at either, but at comparable institution). The highest non-completion rates are self-funded students. And if students don't complete in the specified time (6 years part-time) universities are penalised. Personally, having had a couple of very frustrating experiences with very pushed part-time/self-funded students, I would be reluctant to take on any more in that way. One almost broke me ... and I'm a rigorous & supportive supervisor.
One way you might make the part-time work is to 'chunk' your time: alternate periods of full-time working with full-time research - say 3 months at a time, or even 6 months.
A PhD is research, not study ...