All debts of the estate are deductible in valuing it: however the funeral expenses take priority over all others. Thus, if there is only £1200 in the estate, and £31,000 of debts, and the funeral costs £1200, all the other creditors can whistle. So, if the DWP pays some or all of the funeral expenses effectively as an agent on behalf of the estate, it has the right to recoup that payment by a sort of subrogation. Exactly the same would apply in the normal administration of an estate where no funds are available until probate is granted, so one of the family members pays for the funeral: they would be entitled to be repaid in priority to all other creditors. That is so even if they did not benefit under the will or intestacy.
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