Perhaps this is what happened.
Nevill and June are in bed. The killer goes into the bedroom via the main door and shoots them both - June five times and Nevill four times (who is either in bed or just by the bed at this point). The killer thinks the job is done and goes back downstairs to reload. Nevill is injured but leaves June and goes down the main stairs to stop the killer. There is a fight and Nevill is injured further. The killer reloads the gun and shoots Nevill four more times. They then put six more bullets in the gun, and go upstairs to the boys room and shoots them. Meanwhile, June tries to make it to the boys' room via the internal door and the killer hears her, so he/she comes back to the main bedroom via that door. June tries to back away towards the main bedroom door but is shot twice more by the door with the two remaining bullets in the gun.
There are now no more bullets, so the killer goes and puts two more bullets in the gun to deal with Sheila ....
Of course, that rules out Nevill phoning Jeremy from the kitchen because he's been shot in the mouth in the bedroom.
It also disregards the bullet case found on the main stairs.
If the blood on the bedroom floor is not Junes, I'll have to rethink it.