That letter is interesting because it tells us of the remorse June felt for how she may have neglected her children throughout her life, and whether she had a premonition of death as was reportedly the case with her husband she still put pen to paper rather than approach Sheila and Jeremy directly. Presumably Jeremy retrieved it from Basil Cock upon her demise, which is why it ended up in the glove compartment under Julie's cognizance and she was witness to Jeremy's comments,namely that he was "glad his mother was dead" but "I do miss the old man occasionally".
Of course there is no corroboration of this account, but it does smack of a man who has put the tragedy behind him and is ready to move on from the burden of the Farm and the bugbear of expectation,which he had endured from the Gresham's days, but now with a vacuum whether temporary or permament filled by foreign trips and the attraction of London city life,yet the reader of all these books on the case is left wondering whether Jeremy would remain happy for long in whatever environment he inhabited post-murders.