I don't believe the conversation took place, I believe it was an alibi to provide a backstory for the police.
I have previously asked about how big the family were and if Colin Cafell was in the picture. There were enough family members available for social services to be involved and Sheila was actively trying to come to terms with her mental state.
Jeremy tried to cover all his bases with his backstory, the build up, the reasons, Neville calling the police during the attack (like if Sheila was going beserk, he'd have time to make two phone calls, let alone one, surely you'd call 999 and just leave the phone running so the police could hear the commotion) and Jeremy accounting for all his movements.
Even Stefan Kizhco got out in the end because it was proven he didn't do it. If Jeremy didn't do it, he wouldn't still be trying to persue it after all this time, he'd have prooved his innocence by now and I'm sure with the developments of DNA and other techniques, something would be able to prove him as innocent.