text: I dont see how a food ratings site, even if it is .gov, qualifies as a definitive source for a borough boundary. As AK53 says the official richmond borough  site confrirms the boundary is correct around the playing pitches. The Twickenham RFC web site contacts page ( https://www.pitchero.com/clubs/twickenhamrfc/contact ) shows a club badge in South road.
  Going to close as hopefully the original question is answered