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.
More top news
The engineering projects will hamper the plans of many people hoping to take advantage of the four-day weekend.
Local media said the location of the crash was among the most dangerous junctions in the region.
London has welcomed in the Chinese New Year in style with the biggest party outside of Asia.