The westbound entry slip from the A329(M) northbound will also remain closed.
The force said the driver rammed a police car during the chase and caused it to swerve and lose a tyre.
The driver – a man in his 30s – was arrested at the scene on suspicion of dangerous driving, attempted grievous bodily harm, driving on false plates, possession of a bladed weapon, failing to stop for police and driving through a red light.
He was taken to hospital, by the London Ambulance Service, where his injuries were assessed as non-life-threatening and non-life-changing.
He remains in hospital and is expected to be taken to police custody at a later time.