Who calls the shots?

Police chiefs responding to criticism about their handling of the recent rioting and looting are queuing up to assure us that they are "accountable".  But accountable to whom?  Certainly not to us - we do not elect them, and have no power to dismiss them (and I wouldn't want it to be so - I've posted before about elected officials being more interested in their re-election prospects than in doing the right thing).  But I've always assumed that they are accountable to the Home Secretary - and yet it now appears that perhaps that is not so.  They are equally queuing up to criticise her for, as they see it, meddling in their affairs, and telling them what they should and should not do.  So just how are they accountable, and to whom?