Yesterday several shops were forced to close in the Carnaby Street area, and parts of Regent Street and Oxford Street. Stores including Liberty and the Apple Store were affected.
EDF Energy described the problems as a 'highly unusual sequence of faults'.
Engineers have been working through the night to repair the faults, but EDF has warned customers they could face further disruptions throughout today.
A spokesman said the faults are not thought to be weather related, but added that the situation has been 'exacerbated by the high demand on the network caused by the continued hot weather'.
Businesses were advised to limit their use of non-essential electricity and turn off air conditioning.
An update is expected later this morning.
EDF's emergency helpline is 0800 028 0247.