it used to be the case that if you were 21mph over the given speed limit, 51 in a 30, 61 in a 40 etc that it was a court visit rather than a fixed penalty. iirc the points could then be between 4 and 6 with a higher fine.
in my case several years ago lots of appologetic pleading with the judge left me with the same 3 points but a higher £100 fine.
dont know how it works these days as im a leason learned non speeder* with no points
honestly