Am I right in thinking that no record was found of Nevill having phoned Jeremy?
At that time the phone company did not send statements with detailed phone billing thus there was no way to establish whether such a call happened based on phone records. This permitted Jeremy to make up anything he desired.
The phone company did dispute one of his claims though. He claimed Nevill was in the middle of speaking to him then the call was suddenly cut off. He left the phone off the hook to support the notion that Nevill was dragged away in the middle of the call. Jeremy claimed he hung up and then immediately tried to phone Nevill back but the phone was busy.
The phone company said that if Nevill had been dragged away with the phone left off the hook then Jeremy wound have to have hung up the phone and left it on the hook for about 3 minutes in order for it to clear the line before he could use his phone to call someone else. Thus it would be impossible for him to immediately call Nevill back. If he had been telling the truth he would have had a problem with his phone not working and would have noted such.
As Caroline pointed out this made up phone call harmed him tremendously in the long run:
1) It proved he had contemporary knowledge of the crime- he would have been better off letting people find the bodies in the morning rather than calling police and admitting to having knowledge of the murders at the time
2) The claim effectively renders the killer either Jeremy or Sheila, it prevents Jeremy from trying to blame anyone but Sheila.
3) In addition to not having been able to call back immediately like he claimed, there are several things that defeat the notion he could/would have received such call.
A) If Sheila were running around with a gun why would Nevill leave his wife and the twins in bed? The notion he went to use the phone leaving her to shoot them makes no sense.
B) Even if Jeremy answered it would take a while since his phone was downstairs and take a while for him to dress and come. He would lose 5 minutes making the call and then another 15 for Jeremy to arrive. Why would he think it is better to wait 20 minutes for Jeremy to try to disarm her instead of trying himself?
D) The evidence establishes the event started with both parents being shot in bed and then Nevill and his killer going to the kitchen where Nevill was beaten and killed. The notion Nevill called Jeremy then dropped the phone and went back to bed is not credible at all.