EDF Energy has experienced four faults recently, the latest of which occurred this morning, shutting shops in the Carnaby Street area.
Several Regent Street stores - including Apple Store and Liberty - were sporting makeshift A4 posters informing customers they had shut up shop this lunchtime.
A spokesman for EDF Energy said there will be four-hour periods throughout today and possibly tomorrow in which some of its customers would be without power.
He added the problem had been exacerbated by the high energy demand caused by the hot weather, and urged prudent use of air conditioning.
EDF's emergency helpline is 0800 028 0247.