Or to put it in the simplest way possible, what the officer wrote was correct
That would add the assumption that it was correct, as distinct from thought to be correct by the officer who wrote the log entry.
She did not make her own witness statement about this, it was prepared for her by a police officer who had a mindset to try and conceal the truth
That's mere supposition, but even if correct, it's highly unlikely that the assertion that the operator was not allowed to tie up the 999 system was untrue, as any BT operator would know whether or not such a rule existed. The rule is entirely believable, as the operator had the straightforward alternative of using a normal line unrelated to the 999 system.
. . . changing from being off the hook, into it becoming engaged
There was no report of the status "becoming" engaged. The wording logged was different, that's all.
No, she was asked to check the phone and she reported back that the phone was off the hook
You don't know the exact words that Pc West used. Pc West had dialled the WHF number and heard an engaged tone, which would be the case if the handset was off-hook, even if there was a dial tone on the WHF line. The engaged tone indicates that the line wasn't available when dialled, and only BT can determine the reason why the line isn't available. When Pc West telephoned the operator, it would be natural for him to mention to her that he'd heard the engaged tone (as distinct from an unobtainable tone) when asking the operator to investigate.
Because it was off the hook it wasn't engaged.
That's incorrect. It's always been the case that dialling a BT number results in the engaged tone if there is no fault, but a handset for the number is connected to the line and off-hook. This needn't be true nowadays if you dial a non-BT number, such as a Sky number, but it was true in 1985 for the WHF BT number. The BT operator in 1985 would also get the engaged tone, but could determine the reason for it. I think that the dial tone generated in 1985 would last for several minutes (if no dialling occurred), but not indefinitely.
. . . she would have told PC West that the phone was engaged, and the operator would have been able to obtain the telephone number of the phone it was engaged with, or to.
Had Pc West already mentioned the engaged tone to the operator, the natural response (if the operator had completed her check quickly) would have been to give just the explanation that the handset was off-hook (if no call was in progress). There would have been no dial tone to report unless the handset had only very recently (within a few minutes) been taken off-hook. From Pc West's position, writing "off-hook" was simply the alternative to writing "in use" or "in use" and the type of use, such as "connected to another number".
When the phone is off the hook it is not engaged to an operator, it is simply off the hook with its own dialling tone!
That's incorrect. The operator, unless specifically asked not to dial the number, would start by dialling it, and would receive the engaged tone if it was off-hook, in which case she could then determine the reason for the engaged tone.
If anyone elsewhere tries to phone the phone which has its handset off the hook, of course the caller will receive an engaged tone!
That's true, but the operator would get the engaged tone on dialling the number in the normal way.
She did not hear the dog barking because the phone was not engaged with another line, it was just off the hook with its own dialling tone! . . . the dialling tone would have automatically kicked in after a few minutes, leaving the phone at the farm off its cradle, or off the hook, with a dialling tone sounding in the handset!
That's not what happens. The dial tone commences only when the handset has just been lifted. If a call was in progress and the called party hangs up, the caller never receives a new dial tone by just waiting. If a dial tone ceases for any reason, a new dial tone never just "kicks in". The caller would have to hang up and then lift the handset to get a new dial tone. There's no evidence that it had a dial tone when checked at 3:42am. Even in 1985, the dial tone was discontinued after a short while (possibly a few minutes) unless dialling occurred.