It's believed no Kiwis were on the tram.
Passengers reported the tram had been speeding up before the bend, which has a limit of 12mph (19km/h).
Martin Bamford, 30, from Croydon, said: "Everyone just literally went flying."
He said people were screaming and there was "blood everywhere", describing the scene as "like something out of a film".
Martin Harris, who was on his way to work, told his mother he had been badly hurt, a dead passenger way lying on top of him.
Jane Harris said: "My son was on the tram I had spoke to him for a few seconds and he said that the tram was going really fast. The next thing he knew the tram had derailed and gone over."
British Transport Police assistant chief constable, Robin Smith, said detectives were investigating whether the driver had been asleep "alongside a number of factors".
Initial findings of the Rail Accident Investigation Branch (RAIB) show that the tram came off the tracks as it was negotiating a "sharp, left-hand curve" with a speed limit of 12mph.
An RAIB spokesman said: "Initial indications suggest that the tram was travelling at a significantly higher speed than is permitted."
The Wimbledon-bound tram was travelling from New Addington when it overturned at around 6.10am on Wednesday, London time.
Resident Pat Rooke, 72, described the scene in the wake of the accident as "pandemonium".
She said: "Even my husband was covered with blood," she said.
The last known death of a tram passenger in an accident is believed to have been in 1959. Two passengers and the driver died after a tram collided with a lorry and caught fire in Glasgow.
The death toll equals that of the 2004 Ufton Nervet rail crash in Berkshire, when a car deliberately parked on the tracks in a suicide attempt by the car driver. Seven people were also killed in the 2002 Potters Bar crash Hertfordshire, when an undetected fault on the line derailed the train, and sent a carriage onto the platform.
A spokesman for British Transport Police said a 42-year-old man from Beckenham had been arrested on suspicion of manslaughter and is in police custody.
Finn Brennan, of the train drivers' union Aslef, said the accident was "truly dreadful".
He said: "Lives have been lost and there are many serious injuries. This is a tragedy for all those involved. For the women and men who set out this morning on their journey to work and suffered this awful accident and their families, the grief and pain must be terrible.
"There will be a full investigation. There should be no rush to judgment or to place blame until the facts are known."
The Ministry of Foreign Affairs said The New Zealand High Commission in London was liaising with local authorities to determine whether any New Zealanders were caught up in the tram crash.
"At this stage there are no indications that any New Zealanders have been affected," an Mfat spokesman said.
