"It's very early stages but there is no suggestion yet this was terrorism," the Metropolitan Police told the BBC. "There is no SO [Special Operations] involvement at the moment."
London Fire Brigade station manager Bruce Grain said the helicopter crashed to the street and burst into flames.
"The fire spread to buildings along the road," Grain told the BBC. "We were able to rescue someone from one of the burning cars that the helicopter hit. All the fires are under control now, we're damping down and making the area ready for the investigation."
Witnesses said debris from the crash was flung about the area and plumes of black smoke could be seen rising in the air. The crane was toppled at a construction site.
Transportation officials said train and subway service resumed after a temporary suspension, but a bus station near the crash site was closed.
Sky News said the helicopter pilot and another person were killed.
Officials said the helicopter departed from Surrey and had tried to land in Hertfordshire but couldn't because of fog, Sky News said. The helicopter was thought to have been returning to Surrey when the accident happened.
The Air Accidents Investigation Branch is investigating.
Berkeley Group, which owns the development company for the apartment building under construction, said in a statement, "We can confirm a helicopter collided with a crane at St. George Wharf ... this morning."
St. George's Wharf Tower, where the crash occurred, will be among Europe's tallest residential buildings when construction on the 594-foot, 51-floor building is completed this year, the BBC said.
The residential tower is on the south bank of the River Thames, with apartment buildings and the MI6 (Secret Intelligence Service) building to the east, the BBC said. To the west is the new U.S. Embassy.
"I thought it was a terrorist attack. We were running for our lives," a landscaper told Sky News.
National Air Traffic Services had notified pilots last week about the crane at the construction site at a height of 770 feet above sea level.