I would say ignore what league tables say, and look at the modules for third year. Most unis have very similar courses for first and second year, and third is where they vary. I am personally into the more scientific side so a good research department is important to me, hence why I’ve chosen Durham (99% of research is world class or something similar) and Nottingham as insurance - both have very good research facilities. Most unis will cover cognitive and biological psych in first and second year, so you’re pretty much guaranteed that wherever you go. Third year modules are often more niche and conceptual - I’ve seen sleep/amnesia psychology, psychology of illness, psychology of music etc. Have a look on the website of some unis which you like the look of for the psychology course to get an idea.
Some of the unis which come up top year after year are Bath, St Andrews, UCL, Durham, Birmingham which I’m pretty sure you may have considered already. However, there are some very good non-Russel group unis which have great psychology depts which are often overlooked: Kent for example, or surrey which provide a course with a year in work (which is super useful, and the course isn’t any more competitive - you don’t need higher grades)
Hope this helps and good luck in your application!