Hi! It's a great start that your course is BPS accredited, the next step to becoming a clinical psychologist is gaining clinical work experience and doing a DClinPsy. As of now, there is no other way to become a clinical psychologist in the UK without doing a postgraduate degree. The vast majority of any psychology specific jobs tend to require further education, whether that be MSc, MRes, PhD, DClinPsy, or other certifications. Don't be too disheartened if you are solidly set against doing postgraduate education though, there are still plenty of things you can do with a psychology degree as it is one of the most widely useful degrees available.
-Kat (2nd year psychology undergraduate, Lancaster University)