More times than not people using rhyming slang don't even think of it as being rhyming slang, because the rhyming word isn't used. "Bristols" for breasts for example (short for "Bristol City"); "berk", short for for "Berkshire Hunt".

Rhyming slang with the full rhyme is rare, but I suspect it always was, in daily speech, because it interferes with the original point, which was to be a bit impenetrable.