Under the terms of the Grid Code, National Grid can direct Distributed Network Operators to implement short-term demand reduction measures. The Distributed Network Operators have a number of different tools available to deal with a request of this nature; these include short-term disconnection, interrupting supply to those customers whose contracts permit it or the use of voltage reductions. The severity of the situation would decide which of these measures were appropriate.
However, this is a very short-term measure that can only address an emergency situation. In a long-term shortage of supply incident other demand restraint measures would be utilised.