The silver Vauxhall sustained front and side damage following the incident that happened near to the Pizza Hut delivery shop off Ross Road.
The railings are part of the Meadow Close block of flats. It is understood that another car was also involved in the incident.
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An ambulance and paramedic car were both sent to the scene, as well as marked and unmarked police cars.
A West Mercia Police officer told the Hereford Times that no injuries were caused.
Despite there being a lot of traffic on Greyfriars Bridge heading south, the road is not blocked. We will endeavour to get more information from the emergency services tomorrow (Monday).