IIRC, production Concorde aircraft didn't need the chute as big improvements in braking technology during the prototype phase ruled out the requirement.
Around 1973, two Lightnings diverted into Manston after being launched from Wattisham on "Q". As they were very low on fuel, the fire trucks were in position to deal with any incident and followed them down the runway until they stopped and jettisoned the streamed chutes. Shortly afterwards the tower was informed that one of the fire crew was being taken to the medical centre for treatment after burning his bare hands while manhandling the hot chute.