Police say the accident happened at around 1pm today.
London Ambulance Service also attended and three people, including two members of the public and a police officer who was driving the police vehicle, were taken to hospital.
Their injuries are not believed to be life threatening or changing. Two other members of the public were also treated at the scene for minor injuries.
Jamaica Road has been closed between the junctions with St James's Road and Rotherhithe Tunnel and Traffic officers are investigating the circumstances of the collision.