generic graduate schemes would be open to you (although you wouldn't be a candidate for the more well paid/competitive ones as they will prefer STEM grads)
in the psychology field there is a lot you can go into but most graduate level positions require further training/qualification, as examples - teaching, counselling, clinical psych, educational psych, research, occupational psych, occupational therapy, art/drama/music/play therapy is also a possibility although more difficult as they prefer an undergrad degree in their subject rather than psychology
without further training within the field you're looking at jobs like HCA, support worker, teaching assistant, recovery worker... and eventually things like assistant psychologist posts and IAPT posts
you can get a reasonably well paying job in psychology but it generally takes a lot of work and commitment while in poorly paying jobs/further training to get there
you should have a think about what roles you would actually be interested in doing and what the routes into them would be as I'm not sure what you're actually aiming for if you want to work in the NHS helping people but not be a clinical psychologist, obviously not everyone working in the mental health service is a clinical psych, others will be counsellors, CBT therapists, IAPT workers - but I don't know why you'd want to do those and be opposed to the idea of clin psych!