Two PhD's in different UK universities, simultaneously, part-time: absurd idea?
Andrew mostly covered why this is administratively impossible, but I think it's also worth addressing the misunderstanding of what a Ph.D. is embedded in this question.  Pete Clark said it better than I can, but Ph.D.'s are not merit badges.  More is not better.  Getting a Ph.D. on one of these topics will not stop you from working on the other.  Working with one of these advisors officially will not stop you from staying in touch with the other, and potentially collaborating in the future.  You want to have ideas about other stuff to work on once you finish your dissertation.

I don't envy having to make the choice, and you will have to close one the doors part of the way to actually finish your degree.  But you don't have to slam it all the way shut, and you never know when ideas you know thought you had set to the side will come right back to you.