Hey I'm studying Psychology at Uni now without ever having studied it before! It's absolutely fine because they start from the beginning. Some people that have already studied it will have a slight advantage as they may already know some of the cases but that's only in first year. Schools all have different syllabi so for most people what they study at uni is different to school anyway
The course is pretty newbie-friendly, largely because the first year might as well be A-level Psychology - it's a recap, basically. It builds the foundation for the remaining two years.
You should be perfectly fine without prior academic experience.