Hi London Jane,
I definately think you should keep trying and do not give up just because you did not get one job, you have a wealth of experience and this should not be ignored, I don't think it matters that it is voluntary, many skills in Social Work are transferrable after all. I think the fact that you have had lots of experience in these areas speaks volumes over whether it is voluntary or statutory. I think the important thing is to remain confident, after I graduated I applied for several postions before I got my job and many I did not hear back from for a while. I had an interview prior to getting my current job but got turned down because my lack of experience. I think it is important in interviews that you are able to demonstrate you know the field well, and have lots of experience and how the skills you have developed can be applied to stautory social work.
I do not know about agencies or social work in London so I can't offer you any advice on this, but I wish you all the best with the job hunt!
The Young One.