The intelligent, self-educated working class of that era went on to have children and grandchildren who were middle class, because in that era education did specifically drive social mobility. We've gone from two thirds of the population in manual/routine jobs to well below half
The working class people in these old BBC documentaries always come across as clever and thoughtful individuals, whereas the ones the BBC interviews these days for their vox pops always seem to be complete morons. Either the whole country has become stupid or the BBC is misleading us.