IF (MASSIVE IF) an answer machine was utilised, it would be for the sole purpose of 'answering' a call from WHF at 3.00 (or so) in the morning.
As soon as Jeremy got home, he destroys the tape.
Jeremy almost certainly couldn't be sure if BT would be able to log the call or not, esp not when it came to pulling out all the stops in a murder enquiry, so it would make some degree of sense of for him to actually make sure a call happened (rather than just leave the phone off the hook and hope BT couldn't prove anything).
In order to answer the phone at Goldhanger (without him being there of course) an answer machine would be fine. There would be no voice, since Nevill was probably dead by then AND Nevill's voice on tape would have been no help to his defence.... it would make it worse.
Now, it would clearly NOT be in Jeremy's interests for any recording to be heard, even if silent, since this would only help to establish that he wasn't at Goldhanger.
The only 'worrying' part for Jeremy is that he must make the call from WHF and then get home as fast as possible in order to call the police, then get cleaned up as quickly as possible.
For those that think he didn't make the call, just left the phone off the hook... that's possible too of course but here's the pro's and cons:
Leave phone off the hook only:
1) If BT can prove no call was made, he's in trouble (huge con)
2) There's no tape to get rid of (minor pro)
Make the call (using answering machine):
1) If BT can prove the call was made, he's covered (huge pro)
2) If the tape is found he's in trouble (con)
3) He has to explain 15 minutes between the WHF call and his call to the police from Goldhanger (con)
For me personally, I'd have gone for the answering machine - because I'd be worried about what BT might be able to prove or not. But making no call still seems a very fair option too.
As for the police grabbing any answering machine / tapes...
By the time they'd got around to it, there'd be no evidence. In fact, Jeremy only has to destroy one one cassete tape (the old standard size, or possible a mini sized one). There weren't many solid state machines around in those days.
of course ALL of this presupposes that Jeremy did it.
If he didn't... I can't really see there being a recording of Nevill saying "Jeremy my boy, daddy here, sorry to call you at such an unseemly hour, I wonder if you might get back to me whenever is convenient - it's your sister, she's had a bit of a to do with the rifle. Tally ho!"