A Mitsubishi Space Star was traveling in Cockle Hill when it left the carriageway and collided with a wall at around 4.30pm on Wednesday (November 17).
The driver, a man in his 90s, suffered serious injuries and the passenger, a woman in her 80s, suffered serious spinal injuries.
They were rushed to hospital for treatment.
No other vehicles are thought to have been involved, police said.
Sgt Martin Wilcock, of the Serious Collisions Investigation Unit, said: £This collision has left two people seriously injured and my thoughts are with them at this time
"We are now working to establish exactly what occurred and I would ask any witnesses or anybody with CCTV or dashcam footage which could assist our enquiries to contact the police."
The road was closed for several hours for the emergency services to carry out their work but has since re-opened.
Anyone with information can contact police by calling 101 or emailing [email protected], quoting log number 1050 of November 17.
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