Science can rule people out
Just like Jeremy is ruled about by reasons mentioned above. The same applies to the police they are ruled out because Sheila's wounds are contact wounds and the ammunition used matches the rifle on her body and not the police weapons.
This leaves just one person left and that is herself.
It is what it always has appeared to be, but many people badly wanted it to be another story and for the last 31 years they have succeeded. 
David do you really think:
1) Nevill telephoned his son in the middle of the night to say there was an emergency at the Farm which necessitated his son's diplomatic skills?
2) The Police on duty at Chelmsford deliberately concealed a telephone call from Nevill, which would confirm their boss's initial supposition that Sheila was the killer?
3) Jeremy loved his parents, was blissfully happy with his status at the Farm and had the patience to wait another twenty years for his inheritance, half of which would be shared with a sister he despised?
4) Sheila in the state she was in writing the letters(thanks to Adam for this point) was truly capable of loading a magazine, firing a gun, reloading a magazine, not missing with any of the bullets and all the other paraphernalia involving firearms which I cannot begin to think about?
5) That the gasman on the Monday who witnessed a typical placid domestic scene and Sheila after skipping along with her sons on the Farm perimeter on the Tuesday really had malice in her heart towards them?
6) That Julie, James Richards, Susan Battersby and Liz Rimington ,all of whose anecdotes condemn Jeremy from the words of his own mouth all lied because they had some secret vendetta against this nondescript Walter Mittty-like character who thought then and still thinks to this day that he did everyone a favour by destroying five lives in three generations of one family?