Yes, as tykechick said, local authorities tend to put Social Workers into hospitals so it would be the local authority that would advertise (except in perhaps, some specific examples like Palliative Care/Renal Care, maybe).
Actually as there aren't many hospitals inner London and it's pretty much my 'patch' in that I've been in and out of most of them (for work, I hasten to add) I can say that that is the case!