Police were called to Westminster Bridge at 7.52pm on Saturday, 7 August to reports of a man with a cut hand.
Officers attended along with paramedics from London Ambulance Service.
The man with the hand injury was treated at the scene before being taken to hospital.
It was also reported to officers that a man had jumped into the River Thames from Westminster Bridge.
A search is ongoing to locate this man.
The incident is not being treated as terror-related at this time.