There's a short answer to this and a long answer to this.
The short answer is that in principle Aby necessary background knowledge required will be contained in any specified A-level subjects ans they won't assume any background beyond those. In this case if A-level Psychology isn't required they won't expect any specific background knowledge from it.
The slightly longer answer is that whole they may not require from an admissions perspective or explicitly assume from a teaching perspective specific knowledge, some backgrounds may correlate with better success on some degree programmes and/or they may implicitly assume some level of familiarity with a general background. In the case of psychology for a number of courses (e.g. Oxbridge, UCL, KCL, Bath) the courses are reasonably scientific and so not only do they expect you to have met their entry criteria which usually require a science A-level, but it may also be that students with more scientific background beyond the minimum requirements are better equipped to deal with parts of the course those without that background find challenging - and it may be that the other areas of the course are managed equally well by all students on the course, so in effect having that background is advantageous.
A parallel example also arises among numerate STEM degrees (e.g. physics, CS, engineering) where FM is often not a requirement but may correlate with better success early on the course, enabling students to build stronger foundations to succeed overall on the degree. So while not required, students with that background may find it is an advantage.
To go back to your original question though for psychology I've never gotten the impression it's considered specifically useful to have done A-level Psychology specifically versus just scientific subjects generally (which may in a broad sense encompass A-level Psychology).
It was actually the case about 10 or 15 years ago under an older A-level spec that unis at the time sometimes indicated that it was a bit of a "liability" and they had to "unteach" some concepts which were presented in the A-level in a way which did not represent how the subject was taught at degree level (although I think this is no longer the case).