It is clear the answering machine was switched off.
Jeremy said he was 'sleeping like a log' when Neville rang. It could have taken several minutes for him to wake, realise the phone was ringing, decide to answer it, then go downstairs. Even if the phone rang ten times before it went to answering machine, there is no way he would have made it.
Supporters have stated Jeremy was the laziest man in the world, so it was surprising he answered the phone at all. However he did, probably because it was irritating him due to the length of time it continuously rang. Neville being prepared to wait perhaps several minutes for Jeremy to answer while Sheila went crazy. Just so Neville could say eleven words to him.
Even more unlikely than the phone being answered is the answering machine being switched off.
People have 24/7 answering machines now. Either on their mobiles, or a 1571 service on their home phones. It is just as likely that answering machines in the 80's were on 24/7. This is especially true for a lazy person like Jeremy, who may not want to answer his phone sometimes. Especially if it rings at 3am.
Do other people find it a 'curious coincidence' that the answering machine was switched off ?