Oddly, all the details I can find reference Edgecumbe Hall, not House, but I think it's the same place. Oddly, the listing for this specific gateway doesn't mention the exact name carved on it, but lists it as "GATEWAY ATTACHED TO THORNTON HALL AND EDGECUMBE HALL, RICHMOND HILL".
From wander: Northern Clifton (16 Jan 2021)
Taken: Sat 16 January 2021 16:48
GPS Coordinates: 51.457443336667, -2.61098026