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The person involved died at the scene, at the roundabout between York Way and Old North Road, at around 9pm last night.
Police have told Heart the Royston-based fire engine, that was responding to a 999 call, was turning right at the roundabout and was heading for Burns Road.
It overturned onto the grass verge opposite the roundabout.
All four crew members travelling in the fire engine were treated for minor injuries.
The pedestrian's next of kin have been informed. A few flowers have been laid at the scene.
Herts, Beds and Cambs Road Policing Unit says it is asking witnesses to the collision to come forward, or give them a call via the 101 non-emergency number.
Hertfordshire's Chief Fire Officer, Roy Wilsher, has said: “Our thoughts are with the family and friends of the member of the public who sadly died.
"Hertfordshire Fire and Rescue Service are working with the Police to establish exactly what happened and why.”