In the UK, the Ph.D. is not a clinical degree. The doctorate in clinical psychology in the UK is the D.Clin.Psy so you will not be able to find a Ph.D. in clinical psychology there. I imagine the Brits smile at the Psy.D. versus Ph.D. debates we engage in since they have institutionalized this distinction into their system. However, you can do a Ph.D. in any other area of psychology if research is your thing. Understand however that the educational system in Britain is structured in a very different manner than in the USA. Consequently the Ph.D. process is very different in Britain and most commonwealth countries from what is done here.
The British and Commonwealth Ph.D. is a "dissertation only" research degree meaning there is typically a minimal "taught element" i.e classwork. Instead, your graduate work would consist in mainly doing your dissertation research under faculty guidance. Typically, one needs to have a British-style BA honors degree or a master's degree in psychology to be accepted into a British Ph.D. program. The honors degree is something unique to the British educational system. Their BA degrees are 3 years long and a BA Hons is 4 years long. The MSc degree is typically an extra year beyond the BA. When you apply, you need to find a faculty member whose research interest match your own and who might be willing to supervise your research. As part of the admission process, you write up a research proposal outlining your dissertation topic! So you enter their doctoral programs already having knowing what your dissertation is going to be about and have a general outline of the methodology prepared ahead of time. In some ways the "goodness of fit" between your interests and the faculty member's interests is more important in that system than in ours on this side of the pond.
You are then admitted to the graduate program often as an M.Phil student and after sufficient progress you are "upgraded" to the Ph.D. During this time you are expected to begin publishing, attending conferences etc.. and begin networking. That being said, a doctoral degree from a UK university is very legitimate and likely to be viewed favourably in the US especially if it from one of the well-known schools such as Cambridge, Oxford, or one of the colleges comprising the University of London etc .... It is also important to understand that the Ph.D. can frequently be pursued "externally" without having to be resident at the university itself for 4 years. I have an acquaintance who is getting his Ph.D. in psychology from the University of Kent in Canterbury while living and doing his research here in the US. This is because the degree is awarded on the basis of the dissertation not classroom work. The dissertations produced in the UK are typically far longer and more involved than one typically sees in the USA. If you are looking for academic employment in the USA, you probably would want to stick with fairly well known British schools.