The Metropolitan Police were called to Woodland Terrace in Greenwich at around 3.23am on Thursday.
Officers discovered a blue people carrier, which had been parked outside Benefice of Charlton St Thomas’ Church, partially in the hole.
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police spokesman said no one had been injured in the incident.
He added: “Officers are on the scene and there is a cordon in place. The local authority has been called and there are other agencies on scene.”
A Royal Borough of Greenwich spokesman said the council was working with emergency services to secure the area.
He added: “We are urgently investigating the matter and will update residents the moment we have more information.”
Cleo O’Kane, 25, who lives opposite where the sinkhole opened up, said police told her some residents might have to be evacuated.
She said: “I thought it was thunder – I heard a loud bang, but it was raining so much I thought it was thunder.
“It must have been around 4am. I woke up and then just went back to sleep – my window was open – then woke up at six this morning, came outside and there was a car in a hole.
“I’ve been here for eight years and have never seen anything like this happen.”
She added: “Police said they don’t know what’s going on. They said the car is stuck on a gas pipe or a water pipe. They might have to evacuate all the houses.
“All the car is resting on apparently is a pipe, otherwise it would have disappeared.”
The seven-seater Vauxhall Zafira was left on the road by Ghazi Hassan, who was visiting his brother on Wednesday night.
Mr Ghazi’s brother, Abdul Ahmadzai, said: “He left it here last night after he came round with his wife. He’s on his way here now.”
Mr Ahmadzai added: “I woke up very surprised. The police were here about 4am so I came outside and saw the car – they said it was in a hole. I thought ‘There’s nothing I can do’ and went back to sleep.
“I just woke up again now.”
Asked if his brother was angry or upset, Mr Ahmadzai said: “No, he knows there’s nothing he can do. He just wanted to know if there was any damage, I’m sending him a photo now.”
His brother had owned the car for three or four years, he added.