Do inbounds fly over Richmond Park at all on approach surely it is two far to the south to be on final for 27L they most definitely do fly over Old Deer park which is the big green expanse running along the south bank ( the thames runs S-N at this point so the south bank is really the east bank) and then the extended centre line runs north of Richmond station and pretty close to and parallel to the main Richmond to Waterloo line. 27R of course is to the North and the approach runs south of the river (back on its normal orientation again) over Kew Gardens .
Departures on easterlies however do fly over Richmond Park at the Kingston end