A red Ford Focus and grey Volkswagen Golf were involved in a crash on Ferrybridge Road on Wednesday, August 2.
They were travelling in the direction of Castleford when the collision occurred.
The impact pushed the Golf onto the pavement and it hit the lamp post.
Debris injured several people walking nearby.
A woman, aged in her 20s, sustained serious injuries to her hand and ankle and a man, in his 30s, suffered a serious back injury.
Both were taken to hospital for treatment, alongside the driver of the Golf.
Police, who were called to the scene at around 9.15am, have today released details of the incident as they continue their enquiries.
Anyone with information is asked to contact the Safer Roads Team on 101, quoting reference 13170354565.