800ms looks like it is actually pretty fast for a sober human driving [1]:
"This study examined the effect of brake and accelerator pedal configuration on braking response time to an unexpected obstacle. One hundred subjects drove in the Dynamic Research, Inc. (DRI) Interactive Driving Simulator through a simulated neighborhood 21 times, each time with a different pedal configuration. Each subject was presented with an unexpected obstacle only one time, for one of three previously selected pedal configurations, to which he or she was instructed to brake as quickly as possible. Foot movements were recorded with a video camera mounted above the pedals. Data were analyzed manually, using time and course location information superimposed on the video data. Response times were analyzed using ANOVA to determine effects of pedal configuration and various driver factors. Response times ranged from 0.81 sec to 2.44 sec with a mean of 1.33 sec and a standard deviation of 0.27 sec. There was no significant effect of pedal configuration on response time. Driver age was significant, with increased age corresponding to increased response time. Car normally driven, gender, driver height, and shoe size had no significant effect"
[1] "Braking Response Times for 100 Drivers in the Avoidance of an Unexpected Obstacle as Measured in a Driving Simulator"
https://www.humanbenchmark.com/tests/reactiontime/statistics