Lorna
From your post it sounds as if the DWP consider you to still be in possession of at least part of the inheritance, even though you may have disposed of the money, the DWP can consider you to still be in possession of it if they believe that you disposed of it with the intention of reclaiming benefits and example of this would be your paying your mortgage off early, although the rules are complicated and at the discretion of a DWP Decision Maker.
So you can make a new claim for ESA(IR) but I would expect you to have to show how you have disposed of the money.
Were you asked to do this as part of your appeal? The Decision from your appeal should have given you some idea of how much money the DWP still consider you to be in possession of.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems