There is no solid alibi either side of the coin.
He was a bloke who lived alone in a cottage.
His weakness was he had to rely on the time factor in police not suspecting he had walked or cycled to White House Farm, commit the murders then get back to Bourtree Cottage, change apparel, appear normal to all concerned. He had to delay entry because by necessity Sheila dying by her own hand meant just the one bullet, though as it transpired Jeremy used two, though I wonder whether he was aware of the statistics for people who commit suicide by firearms using more than one bullet (I believe David1819 wrote a post on this several years ago but as I'm on ignore that point will have to be left floating in the wind).
He had to hope Sheila had bled to death by the time the Raid Team entered.