Delgado confirms in his statement that there was a key in the inside lock to the back door. That, then, provides a potential reason for Nevill running for the kitchen. But Nevill was in pyjamas and barefoot. What good could he have done running outside in the dark? Maybe he was running for the den instead (where I think the gun cupboard was, if I'm not mistaken)? He could have barricaded himself in there.
My further questions:
Why are there blood prints near the phone, and blood on the floor near the phone at the other side of the kitchen, discrete from the blood collected near Nevill? If Nevill didn't go for the phone, who left that blood there?
If Jeremy replaces the key on the back door, how does he get past Nevill's body to do this? My understanding is that Nevill's body blocked the interior door between the kitchen and back hallway. How does Jeremy do this without leaving blood on the floor?
If the gun cupboard was in the downstairs office/den, again, how does Jeremy get past Nevill's body to return the silencer? And how does Jeremy do this without leaving a trail of blood on the floor and in the gun cupboard? As far as I know, the only blood is found in the silencer itself.