Police say the crash happened at around 7.40pm on Monday, February 26 when a Vauxhall Astra allegedly failed to stop for officers in Hamilton Street in Blackburn.
Patrols are reported to have pursued the vehicle towards the junction of Albert Street and Peel Street, where the Vauxhall was involved in a collision with a Peugeot 108 car.
The driver of the Peugeot, a 30-year-old woman from Blackburn, suffered chest injuries, while two passengers were also injured. An eight-year-old boy suffered a broken arm, with a three-year-old girl suffered a minor facial injury. All were taken to Royal Preston Hospital for treatment.
The driver of the Vauxhall, a 26-year-old man from Blackburn, suffered minor injuries and was taken to hospital for treatment. He was later discharged and arrested on suspicion of causing serious injury by dangerous driving.
Police say a second man was later arrested in connection with the collision.
Sgt Finn Quainton, of Lancashire Police's Roads Policing Unit, said: "An investigation is underway following a serious collision in Blackburn.
"A number of people have been injured and we want to establish exactly what has happened.
"If you witnessed the collision, or saw the Vauxhall in the area before the incident, please contact us."
Anyone with information can contact police on 101 quoting log reference 1119 of February 26.
Arslan Raja, 26, of no fixed abode, has been charged with two offences of possession with intent to supply Class A drugs, handling stolen goods, causing serious injury by dangerous driving, driving while disqualified, failing to stop and driving with no insurance.
Hassan Khan, 19, of Lynwood Road, Blackburn, has been charged with aggravated vehicle taking and two offences of possession with intent to supply Class A drugs.
Both are due to appear at Blackburn Magistrates' Court on Wednesday, February 28.
The road was closed for more than five hours while accident investigators attended the scene, with the incident referred to the Independent Office for Police Conduct (IOPC)