In R(SB)4/91 the claimant was trying to argue that because the DWP had wrongly paid his mortgage interest for a period (the mortgage was to fund a business) they were estopped from refusing to pay any more once they realised their error. Estoppel could not apply because the claimant " is contending is that the estoppel would give him a claim against the Department for benefit to which he would not otherwise be entitled". DWP clearly cannot be estopped from doing something which they are required to do by law, in that case to calculate benefit correctly.
Your case seems to be different. The law does not require DWP to recover overpayments, it simply gives them the power to do so. If they have said that they will not recover an overpayment they are, on the face of it, bound by that, and estoppel should apply in the same way as it would in any other situation, the DWPs status as agents of the Crown being irrelevant.
That assumes of course that the question arises in the contaxt of actually recovering an overpayment, not in the context of whether the overpayment is recoverable in the first place.
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