Hi, I'm a final year psychology uni student who has also taken psychology at a school level. I would say that it is not necessary to take psychology at the school level, for my University, the modules in the first year of first semester the modules were more general that weren't necessarily psychology based but are areas important in psychology. For instance, the modules I took covered areas in philosophy, biology, statistics, and research methods. The lectures covered things like Aristotle, Synaptic transmission, and ANOVA (statistics). Later on, the modules became more specific toward psychology i.e. in the final year we have a module called 'Neuroscience of mental health' discussing neuronal mechanisms underlying various psychological disorders such as depression, and how these mechanisms inform us about treatment methods which build up on knowledge taught from previous years.
I wouldn't say you will be put at a disadvantage if you have not taken psychology before. I remember initially struggling with coursework because in school-level psychology your arguments are backed by generic comments like "low ecological validity" and stuff, but at the university level, you are encouraged to explore beyond that. For instance, what are the literature gaps in this research, why is this important and what can future research do to explore this? So getting into that mindset took a while.
I feel like psychology varies between universities and the way it is taught, but unless your university states that you would have needed to previously take psychology, I think you are fine. You can try emailing the programme directors of the course if you wish to know any pre-preparation if needed.