Becoming a Psychologist is a far longer process than going to university and getting a degree, or even a masters at that! If you have a preferred area of research, or a preferred area that you'd like to work in then look for universities who have academic staff related to that field.
For example, I chose my university because I wanted to work with athletes so being able to do a Sports Psychology degree with academics who are actively working with athletes was important to me.
Also even though most Psychology courses are BPS accredited, the form of assessments have vary so if your strength is exams, then chose one with more assessments based around exams as it could mean the difference of graduating with a 2:1 or 1st.
You could also look at doing a degree in an unrelated subject and then going a Psychology conversion course at MSc level to get your the accreditation you need to work as a Psychologist.