I have a degree in Sociology and an MSc in Psychology so I might be able to help.
There are a few common routes into social work which are to do the degree in that, or to do a master's in social work once you have completed a more generic degree like the ones mentioned. There are also a few fast-track programs for people already with a Masters which would usher you into social work with more study (there is a bursary for this, the last time I checked it was around £18K depending on the provider).
A Psychology degree alone does not give you a huge advantage in the employment market as the market is saturated with graduates in that area. People who do Sociology tend to go into roles such as teaching, research, or local Government.
I would check how much experience they require at the Universities of your choice, I know providers who will take people with no relevant experience at all for social work