According to https://www.royalparks.org.uk/__data/assets/pdf_file/0010/65395/160812_CPB_cycle-policy-TRP-2016-approved_es.pdf (Cycling in the Royal Parks Policy Statement 2016)
Speed limits do not apply to cyclists within the parks but it is recommended that cyclists keep to appropriate speeds for the environment
I guess that came out after this
https://www.standard.co.uk/news/london/london-cyclist-fined-for-speeding-in-richmond-park-after-he-is-clocked-at-38mph-a3102191.html
@jellybaby started
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According to https://www.royalparks.org.uk/__data/assets/pdf_file/0010/65395/160812_CPB_cycle-policy-TRP-2016-approved_es.pdf (Cycling in the Royal Parks Policy Statement 2016)