We were only playing leapfrog was the version I knew in the mid-late 1940's. My Uncle's who along with my Dad had been at the war, often used our home as a staging post on their way home to and from the forces whilst awaiting demob. We lived near a rail station and their family home was in the sticks some miles away, and they would sing that song to me whenever they were about.Years later they used to watch me play cricket and I used to recall that song whenever I saw them sitting on the benches around the ground.
Thanks for the memory, albeit I am a bit late in seeing it and responding!!