Without doing a Masters, and assuming you achieved at least a 2.1, I have worked with BSc Psychology graduates employed in HR, various roles with Looked After Children, Criminal Justice, counselling roles, substance misuse intervention and prison rehabilitation services.
That is a quick, off the top of my head, list of roles that I have directly come across. There is a thread from a few months ago with a link to LOADS more roles. Anyone that says that positions are limited for psychology graduates, frankly does not know much about the flexibility of the qualification.