Theatre shows were cancelled and shops closed as tourists and shoppers tried to enjoy the capital's night life.
UK Power Networks said 2,300 properties had been affected by the blackout which began at 17:16 GMT.
The network operator said power had been restored shortly after 21:00 and apologised "for the disruption this caused to everyone's evening".
Aladdin the Musical at the Prince Edward Theatre was one of several shows where ticketholders were told they would be given refunds after the shows were called off.
Electricity was earlier restored at shows such as Harry Potter and the Cursed Child where audience members were advised the performance would start late.
Theatregoer Sarah Ellacott said there had been "rapturous applause" at the theatre when the power returned.
Kurt Pollington, 56, who works on nearby Bond Street said there was a "weird atmosphere" throughout Soho while a lack of working traffic lights had caused "gridlock" around Shaftesbury Avenue.
The power cut did not affect the Tube network, according to Transport for London (TfL).
UK Power Networks said: "An underground electricity cable has faulted on our high voltage network causing an area wide power cut."
Black Friday took on another meaning in central London when a power cut plunged a large part of Soho into darkness.