I was wondering if anyone could shed some light on the origin of the phrase in title.
1 is the closest to being correct here.
It's an East End London idiom.
It is used when someone is very angry & arguing, & sticking their face right into the person that they are angry with/complaining to. Therefore, telling someone to "wind your neck in son, and calm down", is to literally tell them to move their neck back so their face is not in the space of your face, & this is generally followed by an explanation of why the "aggressor" is upset because of incorrect information.
It's neither common nor a well-established usage, so arguably the exact sense is somewhat subjective. @mplungjan's link gives us...
1: Don't get upset when you've no real reason to be upset
...whereas Urban dictionary has...
2: Given as advice to someone you you'd like to sit down and shut up
...and (thanks to @Josh61's comment below)...
3: Don't look where you're not supposed to (i.e. - "Don't stare", or "Don't rubberneck!").
My guess is that #2 is probably a better definition, since I assume the expression has its roots in stick one's neck out (to take a risk, alluding to putting one's head under the guillotine), coupled with poke one's nose in (show unwelcome interest in someone else's private business) and stick one's oar in (make an unwanted contribution to a private debate).
In short, if someone says "Wind your neck in!" they essentially mean "Pipe down!". Maybe they're annoyed by you whining about being upset, or repeatedly asking stupid questions. But whatever it is you're saying, for whatever reason, the other person doesn't want to hear about it.
EDIT: The earliest written instance I found was this from 1955 - clearly matching Eric Partridge's 1984 definition ("Stop talking!", RAF slang from the late 30s). But you'll have to decide for yourself whether other more recent usages with different senses are "errors", or "new coinages".
A long time ago I was serving a custodial sentence. Anyhow, while the prisoners were locked in their cell they used to talk out of their windows while sticking their neck out. "wind your neck in" was often a phrase of banter. Therefor, I think it is very much possible that the police officers have actually got the saying from the potential prisoners