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?
Join the Team Zwatt campaign for a discounted power meter - available single-sided or dual-sided!
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10 September 2017 (Sunday): Springfield Cross
16 September 2017 (Saturday): Push Sports MSG Cross