If he hadn’t made up the thing about his dad ringing him saying Sheila had gone berserk with a gun. When it was found by the time he’d gone downstairs to make the call he’d already been shot twice in the mouth.....so wouldn’t have in all likelihood either be able to speak or be ringing Jeremy....he’d have dialled 999.
If Jeremy had just done it and left the bodies there with the house supposedly locked from the inside he’d have had more chance of getting away with it. Guess he was trying to stage an alibi.