Check this website.
http://www.jobs.ac.uk/jobs/psychology
I know a lots of students start their PhD immediately after their UG and some do after Masters. My suggestion is start talking to Professors and they may direct you to more information. A lots of time, Profs have funded projects. Not sure how it works when it comes to prove that your phd is your original work. Thats to discuss with your advisor.
Good luck!