Television images showed a blue tent-like cover placed over the vehicle, which was parked outside an American Express foreign exchange office.
A report said doormen from a nearby nightclub had reported that someone had crashed a blue Mercedes sedan into garbage bins and run away.
Jack Straw, who was named justice secretary by Gordon Brown, Britain's new prime minister, said ministers had been informed of the incident and called it "very saddening," but added "these things happen."
The area around the vehicle was cordoned off as a precaution on Friday morning while explosives officers examined the vehicle.
London transport officials said the Piccadilly Circus Underground train station was closed.
The alert comes a week before the second anniversary of the July 7 London bombings, in which four British Muslim suicide bombers killed themselves and 52 bus and subway passengers.