I think that in writing about her own experience Julie Burchill she hasn't really reflected that her experience was very much a product of that time.
ie post WWII after the attempts to get the UK back to what it had been before WWII ie class and sex rules re-establilshed not only failed but promoted a backlash. ie women resented being told to go back to the kitchen (the main spring for what became WLM) and working class people had been expected to take up roles and responsibilities to help the war effort, weren't going to be told to go back to their traditional roles of just obeying orders.
The media may have been the sphere where the voices and experience of the working class were most obvious in late 50s early 60s, but in them becoming icons it spelt the end of their prominance. So for young people growing up during that time who aspired to be like them, found that as has ever been the case, having middle class or even upper class links gave them a head start.
And inevitably those who were sucessful became as it were "middle class". So the class order re-established itself.
ie the middle class stays entrenched but has fads when it promotes outsiders, once it was the working class, then it was women, then Black people and now ... trans / queer?
Also not sure how you define working class now. Partly because the communities that fostered a sense of being part of that class and having its own values and role models have been and are being destoyed by gentrification. Many of the jobs that were traditionally thought of as working class dont exist any more ie even if low paid, at least jobs with contracts or through the apprentice system something you could count on through your life. Now low paid jobs are all short term contracts or worse, and are as likely to be done by members of other communites, ie Eastern European, Bangladeshi.
One place that maybe what is still the working class now have an opportunity is reality shows, some of which I am sure the producers thought would make the participants objects of ridicule, but have become aspirational??
(I think this is a more urban reflection, and am not sure that what has / is happening in the countryside is the same.)