Traffic was at a standstill around Wellington's Customhouse Quay on Friday afternoon after a speeding driver got into an ugly fight with the man who confronted him.

The man at the centre of a road rage incident on Wellington's Lambton Quay, which left two people in hospital, has been charged with reckless driving and assault with intent to injure.

Police confirmed on Saturday that charges had been laid over the incident and that further charges were likely to follow.

Two men were taken to hospital on Friday night after a man seen driving at dangerously high speeds through downtown Wellington allegedly assaulted a man who complained about his driving.

A witness described seeing a man in a red Mini speeding down Willis St at about 4.30pm on Friday at "about 120kms and almost hit people and cars".

"Finally he stopped, and the courier driver he almost hit chased the car and took his keys," she said.

"The bad guy chased the courier driver into a building, beat him up, then jumped from the second floor and broke what appeared to be both his legs."

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"The bad guy crawled out on to Customhouse Quay where we had to restrain him until the police arrived."

Witness Jack Price was crossing on the green man in Willis St when the car came within a metre of hitting him.

"He almost killed me, I swear to God, I reckon he was going about 80kmh," Price said.

Another witness said it was very lucky no-one was killed.

"I've never seen anything so dangerous. Crazy driving with people having to jump out of the way."

Police confirmed the man was in a small red car, driving northbound at excessive speeds along Willis St through a southbound bus lane.

"Several pedestrians had to move out of the way to avoid being hit as he went through red lights.

"The speeder was stopped in traffic merging onto Customhouse Quay and was then confronted by a man about his manner of driving.

"He abandoned his vehicle and followed the man into a nearby building, where an alleged assault has occurred."

Police arrived at the scene to find the alleged offender with injuries as he left the building.

The man is currently under police supervision in hospital with moderate to serious injuries.

The other man, who was still inside, was taken to hospital for observation.