To be in for the high jump is to be in line for serious trouble, so it seems most unlikely that the phrase is connected with jumping in athletics or steeplechasing. Instead , the high jump here is probably a slang term for hanging, referring to the convicts drop (hardly a voluntary jump) when the trapdoor is opened on the floor of the gallows platform. To be in for the high jump, then, was formerly to be in for very serious trouble, indeed.
There is one other possible explanation: children traditionally jump about in pain after a spanking or caning. To speak of being in for the high jump was perhaps originally to anticipate a painful hiding and its aftereffects.