The first step in finding a distance-learning Ph.D. program that matches your research interests and suits your needs is to figure out what you want to study, find schools that have those programs, then find professors in programs you want to work with. Then you can contact these professors to talk about whether you are a good match. This is also a good time to bring up the distance-learning option, or partial residency if full distance-learning is not an option. Faculty members that you have identified will in turn advocate for your admission. See a link in Resources for schools in the U.K that have distance-learning Ph.D. programs.
Though some schools offer you the distance-learning option, don't ignore a good program just because it is not labeled distance learning. Many Ph.D. programs give you the option of nonresidency during your dissertation research. This means that for a three-year program, you may only have required residency of one semester, or at most one year. You can conduct your dissertation research from anywhere as long as you are in touch with your adviser who approves. This is, of course, if you are working on something that does not require your physical presence on campus, such as being in a particular laboratory, for example.
Some schools in the U.K offer a Ph.D. for substantial work that you do on your own that has been published. Some of these schools limit such programs to school alumni or staff. See Resources for such schools.