I think that you should be pointing out to the Social Services that if they have been billed by the care company for care that you did not receive, then that is potential fraud and it is the care company that Social Services should be looking into, who must have been supplying them with time costs when they attended you.
Also that seems a heck of a charge by Social Services of roughly £158 pound per week towards your care package. I think I would be checking that one out as well.