The integration of distributed energy resources (DERs) leads to several technical challenges including capacity limitation in the low-voltage (LV) distribution networks. Different control strategies are being widely developed to influence individual prosumers, i.e. small active consumers /producers, to facilitate demand response (DR) mechanisms. However, most of DR mechanisms focus only on employing the flexibility of the prosumers, while neglect or partially address physical constraints of the distribution networks. This paper proposes a ‘graceful degradation’ concept to complement the DR mechanisms in solving the network congestion problems. The proposed mechanism is based on an advanced power curtailment mechanism which is verified by a numerical simulation of a 24-bus LV network.