You should try some local authority websites. They usually advertise when the last onslaught of workers leave. This phenomenon usually occurs every 2-3 years.
I was a Social Worker for Glasgow City Council for a number of years after completing a post-grad. There are always opportunities at certain times.
Most councils will advertise for Social Care Assistants and will offer training in Social Care and Social Work. However, you would be contracted into a job for some time if you were to take this route. The hook is that your course would be fully paid for by your employer. Some care organizations also offer opportunities for training, but the same principle applies.
You could self fund via student loans etc, but I do not understand how you would gain the 4 years training on a part time basis. For a first degree in Social Work I thought that the training was 4 years on a full time basis. Post-grads are generally 2 years full time.
Whatever happens,
All the best,
Social Work can be a rewarding experience and the pay is pretty good too.