Police can detain the suspect for 24 hours before being charged, released or released on bail.
The car is believed to have passed through Whitehall from Trafalgar Square before reversing into the opening to the Ministry of Defense car park and then pointing towards Downing Street on the opposite side of the road.
Simon Parry, 44, who witnessed the incident from his vantage point at a protest opposite Downing Street, said: “I heard a bang and looked up to see loads of police officers with Taser guns yelling at the man.
“Many police vehicles came very quickly and were very quick to evacuate the area.”
He said the driver was facing the floor when he was arrested.
Mr Parry said that when the car hit the gate: “Many children ran away, the man was quickly seized by the armed police, they dragged him out.”
He said the suspect “didn’t look like a terrorist”, adding he was told he was wearing a Winnie the Pooh T-shirt.
“He looked like someone who had just had enough and had a bad day and thought he’d try,” said Mr Parry.
Another protester said the driver looked like “a pretty normal person”, adding: “He didn’t look sad, he looked like he’d had some sort of episode or something.”
Large parts of Whitehall were closed to the public and vehicles, with cordons in place, in the immediate aftermath.
‘Long list of disorders’
The incident took place at a time when many officials were leaving their offices, while tourists were also around.
Chris Loder, a Conservative MP, expressed concern that petty crime in the Whitehall area was being ignored and that Thursday’s incident was “just one of many afflictions”.
Mr Loder told The Telegraph: “Most working days I speak to the police about situations that have gotten out of hand at Whitehall, whether it’s the vandalism of the Foreign Office last week, assaults on police officers, suspicious devices, the disrespecting the cenotaph or constant extremely loud music all day long which the law on public order has empowered the police. But they ignore it.
“The senior officers of the Metropolitan Police are turning a blind eye to large-scale incidents in Whitehall. They even allowed protesters to stay on the sidewalk while everyone else was evacuated.
“I will be writing to the Police Commissioner and Home Secretary about this ongoing situation as today’s incident is just another of a long list of disturbances in Whitehall.”