Another issue in terms of household income and inequality is the rise of women in the workplace. You generally find that young educated professionals will generally have relationships and marry other young educated professionals, meaning that two good jobs go into the same household. This naturally increases the inequality between households with well-paying jobs and households without them.
Obviously women should be in the workplace with all the same opportunities as men, but it does widen the gap between the haves- who'll now have two "good" jobs- and the have-nots who may not have any employment.
As for the "hollowing out of the middle class", I don't think that is what is happening. Professional roles aren't disappearing- you can't automate a doctor or a teacher- it is the "lower" manual roles which are disappearing. Which has the effect of increasing competition for jobs that are available which then has the effect of reducing wages down to penury levels and removing any semblance of job security, e.g. care workers, retail staff, delivery couriers.
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If the elite can just up sticks with it's capital, one wonders what incentive there is for it to improve living standards amongst the wider population.
Indeed, and that is what we are seeing in the south east with capital from all the world's dodgiest countries (China, Russia, Saudi Arabia, Singapore) flooding into the London property market. It's trashing living standards in the country the capital has left and it's trashing living standards in London and the south east too.
A 5000% property tax on non-UK residents would solve most of the problems in London, but the elite who run London are the same elite who have stolen all the money out of China and Russia.