Hm! So he gets a silly o' clock call from his panicked father who tells him his sister has gone mad and got hold of a gun, and to please come quickly......................and Jeremy thinks it ISN'T an emergency so the local plod on his push bike -or Ford Anglia if there's one available- will be enough back up?
If that phonecall happened, I can imagine it would have been very confusing for Jeremy.
First, he was half asleep, secondly, he must have wondered why his father called him and not the police and deduced that the situation couldn´t be all that serious, still serious enough to call the local cops, thirdly, there had been incidents in the past where Sheila had a breakdown during the night.
I do think he called Julie, because he did not quite know what to do. She didn´t take his call seriously and told him to go back to bed.