Used for intimidation, and occasionally made somewhat true, this chant is meant to inform the party that the chant is directed at that they will be suffering bodily harm if the chanters' have a chance to inflict it. It is used at the start of the Specials' song 'Concrete Jungle', as presumably a person living in the location the song describes would hear this chant more often than most. The choice of words is probably a poor one - rarely if ever do ambulances take patients to their residence if they have incurred a savage beating.

The chant itself is said with a similar rythym that is favoured by soccer fans (the last 'DAH DAH' being replaced with "Ole"!), which is also present at the start of the aforementioned Specials song and for the start of the Ramones' 'Do You Remember Rock 'n' Roll Radio?'. The movie 'The Italian Job' has all the prisoners in the jail clapping their hands to the rythym , and replacing the last two notes with "Bridger" (as Mr. Bridger was able to mastermind a gold heist while in the clink)

Here is the initial rythym:

dah dah da-da-dah da-da-da-dah DA-DAH

And here is the rythm and the breakup of words as pronouced:

dah da-da-dah da-da-da-da-dah dah DA-DAH

you're go-ing-home in-the-back-of-an Am BU-LANCE

Note that you can say the chant to the original rythym, but it doesn't have quite the same flow.

Football hooligans and punks often use a slightly different selection of words and an altered rythym:

You're go-ing home in a fuck-ing am-BU-LANCE

Or: you're gon-na-get-your fuck-ing-head KICKED IN

This is perfectly acceptable and in the case of the latter it is also a better choice of words.
In Australia, when someone is getting in trouble with the police (especially if you don't like them), an alteration on the original chant is used:

you're go-ing-home in-the-back-of-a Div VY-VAN

(Note that the 'v' is held over the gap (Div vy), but it is not loud enough to hear over the noise that is likely to be present).

A divvy van is a modified ute with an enclosed cage in the back to put rowdy troublemakers who may pose a hazard to police in a regular police car. Again, divvy vans are unlikely to take you home.

Zerotime says: I've heard it as "paddy van" (or "panel van", from bogans), but that might just be some weird WA subset.

CatherineB says: Or 'London ambulance', as heard outside Queens Park Rangers' stadium on match day from the mouth of a boy whose voice had not yet broken...

Positively poetic.

Sideways says: In Fast Forward (the comedy show from the 80s) they used to do a parody on this as 'you're going home in the back of a whippy van' (as in, a Mr. Whippy van.)