I'm not so sure, so I contacted the BBC (as Mr Parris is a long-serving Radio 4 presenter) to ask what action hey would take.
You can contact the BBC (Radio 4) directly using their BBC Programmes Feedback Form. Here is what I asked:
Will you be considering Matthew Parris' position on various Radio 4 programmes, following his outspoken and inciteful remarks regarding cyclists?
14 September 2019 (Saturday): Iceni Velo 10-mile time trial
15 September 2019 (Sunday): ECCA 25-mile time trial
22 September 2019 (Sunday): Godric CC 25-mile time trial
|Learning basic skills :|
|Getting into shape :|
|Fun and safe riding with others :|
|Training for races :|
|Not at all :|