Other roles you can go into with a psychology degree may not require accreditation but it's better safe than sorry as you never know when your career plans may change or what jobs will ask for.
Do you have an idea of what career you want to go into? Some careers for psychology require you to have a BPS accredited degree and therefore it is alot easier if you do a psychology degree that is accredited by the BPS. If you do one that isn't accredited and you wanted to go into a career that needed accreditation you will have to do another course to gain accreditation by the BPS. When I first was looking at universities, I wanted to make sure that the degree is accredited as it saves me extra time and hassle after finishing the degree
I hope this helps and if you have any questions, please let me know!