I'm sure this used to be clear to me but now it isn't! My client was deemed LTAHAW by IS and was therefore deemed overpaid both IS and HB. The IS appeal went to tribunal and DWP decision was upheld. The HB decision has been postponed pending the IS result. In my experience of successful IS appeals, the HBO follows the IS decision, but now I've got an unfavourable IS tribunal decision, can HBO make its own (different) decision, and if it doesn't, is there any mileage in taking exactly the same issue to a tribunal for HB?

The Local Authority is able to make it's own decision however as you rightly pointed out in most cases the LA will follow the line taken by the DWP, particularly where that has been taken to tribunal and the case was successful.