Nutloose
The Commonwealth War Graves Commission commemorates those who died during the First and Second World Wars in service or of causes attributable to service. The designated war years are
First World War
4 August 1914 to 31 August 1921
Second World War
3 September 1939 to 31 December 1947"
As this incident occurred outside these periods I would assume that the CGWC would not have been involved.
Incidentally, The Unending Vigil by Phillip Longworth is an excellent history of the CGWC.