One pedestrian has been taken to Derriford Hospital, via air ambulance, with serious injuries. There are thought to be 7 casualties in total including the driver of the vehicle.
Six of the casualties are being taken to the RD&E for treatment. Fore Street is closed at Long Lane and what is described as the top end of Beer.
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Military personnel are unlikely to be deployed on the streets of Avon and Somerset despite an increase in the national terror threat level.
The major party leaders' campaigns for the General Election will remain suspended on Wednesday following the Manchester terror attack.
The threat level has been raised to critical by MI5's Counter-Terrorism Analysis Centre.