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As far as I'm aware Richmond Park doesn't have nearly the same level of bunched riding - but I'm not a Richmond local
Cycling is currently banned in Richmond Park except for key workers using it to commute (and under 13 year olds).
I ran through it early this afternoon (Roehampton Gate to Robin Hood Gate) and I saw just one cyclist (no idea if they should have been in there or not). It felt utterly empty, I probably only saw 20 people in the 10 minutes I was in the park, less than I'd normally see on that run. Was a little bit chilly and windy though, but nice to run on the road for a change.
The current state of affairs is irrelevant. As far as I'm concerned you should never ride on some random's wheel completely uninvited.