Joseph Leech doesn't appear to have had a coat of arms, and it's not the University of Bristol's (they were another former owner), but I struck lucky with my third guess: the Wills family crest apparently features three martlets around a chevron, as on the right, and three wyverns, as on the left... Can't find anything that's exactly like this one, but them I'm not exactly au fait with heraldry.
George Wills, of the Wills Tobacco family, was Burwalls' owner after Joseph Leech.
GPS Coordinates:
51.45392, -2.63034
Location: Leigh Woods