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Cockney Rhyming Slang is a slang most commonly used by British thieves and traders. Its origin is uncertain, but is thought to come from 19th century London thieves and traders. However, some people believe that it comes directly from East London thieves, who didn't wish to be overheard by the police. With most sentences sounding like gibberish to the casual listener, the code would be rather effective.

The problem in locating its origin, lies in the fact that it is mainly a spoken language. One theory on this lies in the idea that the fewer written logs, the harder the slang will be to break.

Now, some sources claim that it originally used to be a form of Pigdin English. These same sources also say that these days youngsters use the slang more as a joke.

"Cockney" is a derogatory slang word for working class Londoners, and the other two words form the name of the slang quite accuratly. The idea behind the slang is to use a word to rhyme with the word they actually mean. Now this is often taken to greater lengths by taking a popular name such as Brad Pitt, and having the word you want to use rhyme with Pitt. Then when talking in Cockney Rhyming Slang, simply use the first name, Brad. This oughtta confuse those blokes.

You go to your dentist's and he says:

"Let's have a butcher's at that north of yours, china."

Don't worry, all he's saying is:

"Let's have a look at that mouth of yours, mate."

Of course, I still wouldn't trust a dentist that talks to me in Cockney Rhyming Slang.. so.. RUN!
The example's words were chosen from the writeup at the very top.
If you'd like to hear this slang spoken rather convincingly, I recommend renting the movies Lock, Stock, and Two Smoking Barrels and The Limey. Lock, Stock, and Two Smoking Barrels has one scene with subtitles for the reason that the characters are speaking Cockney Rhyming Slang. The DVD for the movie, also contains a small tutorial on the slang. In The Limey, Terence Stamp, speaks the slang in almost throughout the film, but you can still somehow understand what he means.
BBC Online - h2g2 - Cockney Rhyming Slang. http://www.bbc.co.uk/h2g2/guide/A649
Cockney Rhyming Slang. http://www.ac.wwu.edu/~morrelr/cockney.html
History of Cockney Rhyming Slang. http://www.fun-with-words.com/crs_history.html