Micky Flanagan. About as Cockney as it's possible to be.
I'm not so sure you'll find much rhyming slang in the work of comedians though. It's not that common any more. And comedians would want their work to be understood by everybody, rhyming slang was designed to be a bit confusing.
Look up 'Only Fools and Horses', it's a sitcom from the 80s and 90s and the main character uses plenty of rhyming slang. I remember a scene where the phone in his room is broken and he says (to an American no less) 'the old dog's dead.' Dog and bone = phone.