The Metropolitan Police said the 43-year-old, who was also arrested on suspicion of criminal damage, had since been released under investigation but charged with the unrelated offence of making indecent images of children.
He appeared at Westminster Magistrates’ Court on Saturday.
After the hearing, a court official said Kneller was remanded in custody ahead of his next hearing at Southwark Crown Court on June 23.
The Met said: “Armed officers, who were in attendance, arrested a 43-year-old man at the scene on suspicion of criminal damage and dangerous driving.
“He was taken into custody and has since been released under investigation in relation to this matter.
“He was charged with an unrelated matter of making indecent images of children and will appear in custody at Westminster Magistrates’ Court on Saturday, 27 May.”
Rishi Sunak was in Downing Street at the time the car crashed into the front gates, the PA news agency understands.
The Prime Minister, who had been due to leave No 10 anyway, departed after the crash.
There were no injuries reported and police are continuing their inquiries into the incident, the Met said.
Counter-terrorism police are currently supporting officers in their investigation but the incident is not being treated as terror-related, according to the force.
Images on social media showed the car surrounded by emergency vehicles as police cordoned off the stretch of Whitehall outside Downing Street.
Officers were seen searching the boot of the vehicle before a tow lorry removed it from the area.