For some reason, the only British/London expressions I can think of seem to have elements of the salacious or scatological about them.
A piece of piss, for instance, is a phrase referring to a task that is very easy to do. Why it should have taken this form I don't know.
New laddism (as in magazines like Maxim etc) have popularised the dog's bollocks - similar in usage to 'the bees knees'.
Here's another bizarre one - getting on my tits - to mean 'getting on my nerves', or 'irritating me'. Why? Not a clue.
My own 'what does that have to do with the price of...' variant is 'fish'.
I will not bore you with oodles of Bombay slang - since so much of it is not English based.