Police said the helicopter had hit the crane on top of The Tower, One St George Wharf at about 08:00 GMT.
About 90 firefighters were at the scene near Wandsworth Road in South Lambeth. Doctors said one of the dead was the pilot and the other was on the ground. Six people were taken to hospital.
The pilot had asked to be diverted to a nearby heliport because of bad weather.
Metropolitan Police Commander Neil Basu said it was “miraculous” the crash was not much worse.
Burning wreckage lay in the road but the fire was brought under control within 25 minutes, the fire brigade said.
One of those taken to hospital had a broken leg and the others had minor injuries. Seven people were treated at the scene.
Part of the crane was left hanging from the side of the residential building, which is still under construction. London Fire Brigade said part of the tail section of the helicopter landed on roof of the building and the main section landed in Wandsworth Road, hitting two cars. The fire from the helicopter ignited two buildings.
Police said it was understood the helicopter was on a scheduled flight from Redhill in Surrey to Elstree in Hertfordshire.
A spokesman for London Heliport at Battersea said the pilot had requested to divert and land there due to bad weather.
The incident caused gridlock with all approaches to the Vauxhall Cross one way system closed at the height of the rush hour and Vauxhall Tube station and railway station closed, though the stations have since reopened.
London Fire Brigade said more than 50 other firefighters were at St George’s Wharf to secure the damaged crane.
Weather observations at the time of the crash showed very low cloud but not thick fog. The nearest observation site was London City Airport which at 08:00 reported 700 m visibility with broken cloud at a height of 100ft.
NATS, which runs air traffic control across the UK, said the pilot had been receiving assistance earlier in the flight but not at the time of the crash.
The incident will be investigated by the Air Accidents Investigation Branch.
An RNLI lifeboat was initially sent to search the Thames near the crash scene following a request from London Heliport after it lost contact with the aircraft, which is understood to be an AgustaWestland AW109, a lightweight, twin-engine helicopter with eight seats.
Fire brigade station manager Bruce Grain said crews arrived at the scene in four minutes.
He said the helicopter fell into Wandsworth Road, hitting various vehicles and bursting into flames and there were also fires in nearby buildings.
A man was rescued from a burning car by firefighters.
Wandsworth Road was blocked by the burning wreckage and aviation fuel and the side of a building also caught fire.
A motorcycle was also lying on its side in the road where it was abandoned.
Witness Michael Krumstets said: “I was on my way to work this morning with my flatmate when the helicopter crashed right next to us.
“We saw the helicopter clip the crane and heard a loud crack, it started spinning out of control and directly towards us. It took just seconds for this to happen.
“We ran as it fell towards us. We got away just in time.
“We were just feet away when it hit the ground and exploded.”
Mark Osbourne, from a bike shop near the scene, said he ran to try to help the injured.
“There was lots of wreckage and fire,” he said.
“I saw a woman on a motorcycle that must have missed the carnage by six feet.
“It felt like a war movie, it was surreal.”
Craig Dunne, who was walking to work at the time of the accident, said: “When I got to the end of the road there was a massive explosion and the crane is obviously in pieces.
“And I looked to the left-hand side and there were cars – three cars on fire – people screaming, shouting and hollering, and the next thing I know there are police, ambulances and everything everywhere and people going crazy. It’s madness – absolute madness.”
Mark Correll was cycling along Wandsworth Road when debris from the crash started falling around him.
“I heard a massive explosion and looked up to see debris falling everywhere from the sky,” he said.
“I didn’t hang around as there was massive debris falling intermittently and if anything had hit me I would have been killed.
“My first instinct was to dodge the debris – I thought the building was going to collapse.
“It was easily the most frightening thing I have ever witnessed.”
Market worker Andrew Ross said: “I heard a loud bang and I saw this helicopter falling out of the sky.
“[There was] an orange glow and lots of smoke coming up.
“It was flying below cloud cover – it was still foggy and a little bit dark.”
Michael Gavin, who was waiting for a train on a platform at Vauxhall station, said: “I heard the bang – the top of the crane was obscured by the fog so I did not see the impact but I did see the helicopter falling to the ground along with pieces of the crane, then the long plume of smoke from there.
“It was really quite shocking. There was a group of us on the platform waiting, we could not see where it hit because it was blocked by a wall at the end of the station.
“There were a lot of worried people around.”
Nicky Morgan, MP for Loughborough, heard an “enormous bang” as she walked towards Vauxhall Tube before seeing “clouds of black smoke”.
Quinn Murray, who was cycling when he saw the crash, said: “I saw the helicopter hit the top of the crane and come down just to the left of the station.
“There was quite a large amount of fire and a huge smoke cloud. It wasn’t on the road, but into a building site where they are building the new Nine Elms area.”
Erin Rogers, who was waiting at a bus stop outside Vauxhall station, said: “It was a bit surreal actually. I just had a coffee in my hand, I looked up, heard a bang and saw bits of crane debris falling to the floor.
“Then the helicopter was in flames. The rest of the people at the bus station were looking on going <<What was that?>>.
“It’s something I will never forget for a long time.”
The emergency services were praised for their swift response by Councillor Lib Peck, leader of Lambeth Council.
She said: “I understand that swift action by the fire service may well have saved the life of one of the casualties of the crash.
“The safety of Lambeth residents is my major concern and I will be seeking reassurances about the procedures governing helicopter flights.”
Kate Hoey, Labour MP for Vauxhall, said: “My initial thought was that it might have hit one of the many densely populated tall buildings. To hear it had hit the crane was a relief in some way.
“Police said to me that their first fear was it was the police helicopter, however, it had been grounded because of the weather.”
She said the rapid increase in the number of tall buildings in London meant more rigorous controls over who can fly where may be needed.
At Prime Minister’s Questions she asked David Cameron for a review of the rules on helicopters flying over central London.
David Cameron said: “She’s right that it’s not an issue for today but inevitably it’s something that has to be carefully looked at.”
The Civil Aviation Authority said there were 16,374 helicopter flights over London in 2012. It said single-engine craft were required to fly along certain routes, selected to provide safety, and while twin-engine helicopters could operate in wider areas, all were subject to air traffic control clearance.
It said pilots were notified of very tall structures for flight planning purposes, as was the case with the crane involved in the crash.
The Met said there was no suggestion the incident was linked to terrorism.
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