Well, you all voted to have a translation, so here it is. I have written out the lines as L and Watari say them in italics, with the plain English translation in bold underneath. With some words, I go into more depth with the meanings, but if you want to learn the origins of any of the phrases or slang, I am happy to provide information where I can. I've tried not to get too dull or technical here, but apologies if I go off into essay mode.

Another point that someone brought up: L and Watari are actually speaking slightly different dialects. L is using a variant of cockney and Watari has a more Northern tinge to his speech.

So, if you want to know what Watari and L were saying, read on!

If you prefer to leave it as it was, you do not have to read this chapter. Hence, optional.

L: Eyup, dook. What's occurring?

Hello, good friend. What's happening?

Watari: Got grass on yer bloke.
I have information on your man.

L: Giz a butcher's.
Let me have a look. (Giz is actually short for "give us", so he's saying "give us a look". Butcher's = butcher's hook = look; rhyming slang.)

Int this that geezer what skanked the lolly?
Isn't that the dodgy man who stole the money?

The fuzz?
The police?

Watari: Nicked him, but he scarpered.
Arrested him, but he escaped.

Toe rag were int' bog and did an oak table.
Irritating man was in the toilet and vanished. ('Doing an oak table' comes from the British comedy show Blackadder, when Queen Elizabeth mentions that someone vanished, and Percy says "Like an old oak table," to which the Queen remarks, "Vanished, Lord Percy, not varnished." But Percy did mean vanished.)

They caught a gander of the wide boy pinchin' fags from an offie.
They saw the criminal stealing cigarettes from a liquor store. (offie is short for off-licence, which is what liquor stores are called in England.)

L: Bit pikey, innit?
This can't exactly be translated, but it can be explained. If someone has stolen something purely for the sake of stealing that was effectively worthless, it is called "pikey". There's a reason for the expression, but I'd need about a page to explain it. Ask if you want to know more.

Watari: He were somewhat trousered at t'time.
He was rather drunk at the time.

Light squeaks.

L: Well, love a duck!
(an expression of astonishment)

Larry there ent the foggiest what we're blabbering about.
The loner there hasn't got a clue what we are talking about.

Watari: He must reckon we're doolally, eh, mush?
He must think we're crazy, hmm, friend?

L: Oi, poofter!
Hey, person of homosexual inclination!

Soz 'bout the palaver. This blarney must be right bamboozling.
Apologies for all the madness. This language must be rather confusing.

Light: Does my face look bovvered?
This is the catchphrase of the character Lauren from a comedy show called The Catherine Tate Show.

I hope that helped.