I’m in my 30s and certainly still hear rhyming slang used by people my age. Perhaps it is used slightly more “ironically” than it used to be, but people still use it.
Phrases like “Have a butcher’s” are certainly used totally straight and unironically. “Bristols”, “thruppenies” etc are also still in common currency, as is “berk”.
I don’t think there are any such British accents/dialects.
I can’t think of any. But “berk” derives from “Berkeley Hunt”, not “Berkshire Hunt”, as far as I know.
I’ve never heard ball of chalk or battle cruiser - did you just make them up?
But have a butcher’s, apples and pears, jam jar, tea leaf, a cup of Rosie (Lee), Ruby (Murray), would you Adam and Eve it, trouble and strife, barnet, dog and bone, on me Jack (Jones), mincers, thrupennies, and yes, whistle, and several others were in heavy use when I was a kid in the eighties. Some of them are used now. It was only when I was an adult that I found out that some of them - the ones used without the rhyming bits, like barnet, butcher’s and Rosie - were slang and not used in England in general. Then there’s the occasional new one, like an Ayrton for a tenner, from Ayrton Senna.
It’s bizarre of you to say that Cockney rhyming slang was barely being used even in the sixties. 
I don’t think anyone else would agree with you that rhyming slang was uncommon then. It is uncommon now, but not unknown, and not in an “ironic” way either. It’s never been a posh person’s thing of course, or even middle class, but I assume you’re not using posh or middle class people as your barometer for how many people use rhyming slang.
(Just because someone will ask:
Have a butcher’s = have a look. From butcher’s hook
Apples and pears - stairs
Jam jar = car
Tea leaf = thief
A cup of Rosie (Lee) = tea
Ruby (Murray) = curry
Would you Adam and Eve it = would you believe it
Trouble and strife = wife
Barnet = Hair. From Barnet fair.
Dog and bone = phone
On me Jack (Jones) = on my own
Mincers = eyes. From mince pies
Thrupennies = tits. From threepenny bits
Whistle = suit. From Whistle and flute.)
From that very wiki page:
I know that some British accents pronounce it like that because I do so myself.
South London. I hear little bits of Cockney rhyming slang (like the very common words above) all the time, from all sorts of people, and use them myself despite being personally a rather degraded RP, and not from London originally.
Calling someone a berk would be slightly insulting, but would mostly raise eyebrows for being old-fashioned, in my experience. They used it a lot in “Only Fools and Horses”, which I hate. I live in Peckham, by the way.
Do you pronounce both Berkeley and Berkshire as berk-not-bark?
In what part of Britain is that normal? (serious question).
No, I most certainly did not. We’re supposed to be fighting ignorance, not spreading it.
Ball of chalk = walk
Battle cruiser = boozer (pub)
BTW Pig’s ear = beer is still in use for a London beer festival
See also “plonker”. This prime-time BBC sitcom in the 1980s (still a much less permissive age in terms of swearing on TV) had people calling each other cunts and pricks, effectively, and nobody batted an eyelid. That tells you how mild those epithets are.
(Although having said that, when watching repeats of OF&H I am surprised by how close to the wind it sailed at times.)
Rhyming slang can be pretty current (and you can congratulate yourself when you work it out)
Garry… Garry Glitter = shitter (bottom/ toilet)
You used to hear people (men, more accurately) say ‘berk’ quite commonly but it seems to have become obsolete in the last thirty years - perhaps because ‘cunt’ is more accepted than it used to be. I can’t recall the last time I heard anyone use it.
This would be more convincing if there was some plausible connection between “jerk” as “idiot” or “jerkwater” and “idiot”, the way there is between “jerkoff” and “idiot”
I’ve definitely never heard anyone in London say Berkshire with the uh sound (on my phone, can’t do ipa) and it does come up on the odd occasion since it borders London. I’m not sure that wiki page is right.
But “berk” does not mean anything like cunt (nor did it in the '80s or the '60s or '70s, which is about as far back as I can vouch for). A cunt, in Britain, is a thoroughly unpleasant, malevolent person, and certainly someone you are angry with, a berk is a harmless and probably amiable fool, and is often used quite affecionately. I question whether the claim that “berk” is rhyming slang for cunt is true. It is probably a folk etymology. (Not that I have any clue as to what the real etymology might be.)
I would note, also, that “plonker” was used in Only Fools and Horses in a much milder and more affectionate way than I have ever heard “prick” used in real life. Again, “prick” implies unpleasantness and malevolence, whereas “plonker” (as used in OFaH - I can’t say I have ever heard it used in real life), although perhaps a bit stronger than “berk”, signified foolishness and incompetence.
I have never heard Berkshire pronounced Burkshire in London or elsewhere. Nor of Berkely Castle ( the seat of the hunt) being called Burkeley Castle (I hail from Bristol.)
I do however have a memory of the Hunt concerned being called the the Old Berks Hunt with Berks prounounced like the Peerage. I used to attend badminton Horse Trials in the Seventies and think that I heard that usage there.
If that is so, that would give a good provenance for the Burk sound, but I am damned if I know how to substantiate it.
I am in my sixties and have known the association between berk and cunt since I was a teenager- we knew we were pushing at the edge of respectability in the sixties; I suspect that the word has further mellowed over the intervening decades.
You are arguing the same point as me. (Apart from the etymology part, which is well attested.) My point is that “berk” and “plonker”, despite deriving from rude words for the genitals, are mild enough not to shock dinnertime BBC audiences.
Agreed - regardless of their origin, Berk and Plonker are, in common usage, mild terms that typically come up in a chummy, rather than confrontational/aggressive context.
I am in my 60s too, and I do not remember “berk” ever being anything but very mild, and, as I said, not just being a milder version of “cunt”, but meaning something completely different from it. Folk etymologies are often widely known and widely and persistently believed. That does not make them true. The folk etymology that “posh” is from an acronym for “port out, starboard home” has been widely believed for at least as long as that, but is, I believe, pretty much universally rejected by language experts. When explanations sound neat, plausible, and “folksy”, such as by being attached to some “quaint” tradition, like rhyming slang, that is all the more reason to be suspicious, especially when the basic facts (such as that “berk” is actually pronounced differently from the first syllables or both “Berkshire” and “Berkeley”) are actually at odds with the supposed etymology.
I must admit, I’ve not come across Berkeley before, although I do read it as “burkly” in my head.
I’m certainly willing to be proved wrong on the Cockney front - I don’t actually know any Cockneys. My own accent is a curious mix of north Yorkshire and south Devon. I’ve asked my father, who has a strong north Yorks accent, and he says he pronounces it Bark-shire now, because he knows that is right, but wouldn’t have as a child.
My wife, who is from Buckinghamshire, despairs of my pronounciation.