I wish I were an expert on Cockney rhyming slang but I’m not. My mother-in-law lived in the East End of London for much of her life and my husband is a genuine Cockney, having been born within the sound of Bow Bells. My daughter is pretty close to being a Cockney but she was born opposite Big Ben which is a couple of miles too far to the West (and is currently nurturing a Scottish accent, so might not yet be ready to admit her roots in the heartland of the auld enemy).

Films like the (cringingly awful in my opinion) “Carry On” films were full of Cockney rhyming slang – Sid James was particularly expert. Its come back into fashion as part of the “new lad” culture.

Here’s a few that I would recognise:
Apples (Apples and pears) – Stairs
Brahms (Brahms and Liszt) – Tired and emotional
Cream Crackered – rather tired
Dog & Bone – Phone
Loaf (Loaf of bread), “use your loaf” – head
[“use your loaf”= “think about it”]
Mutt and Jeff – Deaf
Natter – Chatter
Nifty - Fifty
North and South – Mouth
Old Joanna – Pian(a) (piano)
Pig’s Ear – Beer
Plates (Plates of Meat) – Feet
Pony (I don’t know why) – Twenty Five
Porkies (Pork Pies) – Lies
Tea Leaf – Thief
Tick Tock – Clock
Titfer (Tit for Tat) – Hat
Trouble and Strife – Wife

They are still being invented, they have always used names from people in the public eye and today is no different.

Here’s a site with a pretty comprehensive listing (including many I’d never heard)
http://www.bio.nrc.ca/cockney/cockney.html

Look up the following(if you dare):
Sherman Tank
Bob Hope
Brad Pitt
British Rail
Dudley Moore’s
Eartha Kitt
Nat King Cole
Ricki Lake
Tony Blair