The incident happened in Stane Street at 9.10pm yesterday (May 10).
Officers were called to the scene and found four people injured.
The driver of a Skoda, a 22-year-old man from Dorking, and the passenger of a Renault, a 19-year-old woman from Carshalton, both died.
The passenger of the Skoda, a 23-year-old man from Dorking and the driver of the Renault, a 19-year-old woman from Billingshurst, were taken to hospital.
Their conditions have been assessed as life-threatening.
Their next of kin have been informed and are being supported by specialist officers.
Sergeant Ian Foxton said: “This is a tragic incident and I would like to express my sincere condolences to the families and loved ones of those involved.
“An investigation is ongoing to establish exactly what happened and we are asking anyone who can help with our enquiries to come forward.
“Anyone who witnessed the incident or events leading up to it, or has any relevant dashcam or CCTV footage, can contact police online or via 101, quoting Operation Select.”
A spokesperson for Sussex Police said: “Police are appealing for witnesses to a collision in Billingshurst on Wednesday (10 May) in which two people sadly died.
“Emergency services were called to Stane Street at around 9.10pm to a report of a collision between a Skoda Fabia and Renault Clio.
“The driver of the Skoda – a 22-year-old man from Dorking – and the passenger of the Renault – a 19-year-old woman from Carshalton – both sadly suffered fatal injuries.
“The sole passenger of the Skoda – a 23-year-old man from Dorking – and the driver of the Renault – a 19-year-old woman from Billingshurst – were both taken to hospital with life-threatening injuries.
“Their next of kin have been informed and are being supported by specialist officers.”
