traffic on the roads around the park is basically back to before now, which makes cycling around that area pretty grim if you can't use the Park. The pollution and congestion probably far more damaging than any social distance non-observance caused by letting people cycle in the park.
Partially: https://www.royalparks.org.uk/parks/richmond-park/richmond-park-news/the-return-of-cycling-to-richmond-park
tldr is any time before 10am and after 4pm, and not on the stretch of road between Kingston and Roehampton (via Robin Hood).