Eloethan, Yes, everyone is allocated into a socio-economic group based on all the factors you mention, but it is getting a lot less easy to do this and these socio-economic groupings, drawn up quite some time ago, are creaking at the seams, as salaries for many professional groups go down in relation to the salaries being earned by others occupationally placed in lower groups and people move more and more between different occupations that mean they keep changing social group as well. My DD recently changed her social grouping in a weekend by changing job and occupation. Her salary remained unchanged.
Anyway, we are not discussing socio-economic groups in this thread we are talking 'class' and I am trying to get a definition about what this actually means, if anything, in the 21st century. In the past 'working class' = blue collar manual work, rented housing, usually council provided, middle class= white shirt, suit and tie, mortgage/owner occupier. But these simple divisions have long gone.
The phrase 'middle class' these days seems to be a word only used pejoratively in a very narrow sense for those privately educated, graduated from Oxbridge with well off parents in quite a narrow group of extremely well paid professions and I doubt more than 10,000 people or so fall into that category, which leaves the rest of the population where?
This question of exactly how you define class in the very occupationally fluid 21st century is the question the OP posed and no one yet has given a satisfactory answer. I can see only one way of overcoming all these problems and that is to band people by income only.