The ABCC1C2DE classifications are very out of date. They used to make some sort of sense, but ignored women, as households were classified according to the occupation of the 'head of the house' who was the man.
Now there are more useful classification scales, including one from the BBC which suggests that there are seven classes in the UK:
Elite - the most privileged group in the UK, distinct from the other six classes through its wealth. This group has the highest levels of all three capitals
Established middle class - the second wealthiest, scoring highly on all three capitals. The largest and most gregarious group, scoring second highest for cultural capital
Technical middle class - a small, distinctive new class group which is prosperous but scores low for social and cultural capital. Distinguished by its social isolation and cultural apathy
New affluent workers - a young class group which is socially and culturally active, with middling levels of economic capital
Traditional working class - scores low on all forms of capital, but is not completely deprived. Its members have reasonably high house values, explained by this group having the oldest average age at 66
Emergent service workers - a new, young, urban group which is relatively poor but has high social and cultural capital
Precariat, or precarious proletariat - the poorest, most deprived class, scoring low for social and cultural capital
More here www.bbc.co.uk/news/uk-22007058.
There are also Marketing classifications which are interested in things like whether people are open to new ideas and trends, and are willing to 'adopt' technology when it is new, or wait until they have seen others use it before taking the plunge (attitudes to risk basically), and others that classify according to spending patterns and preference for tradition and acquisition of 'things' over new experiences.
Class is not about money, and never was, although at one time 'middle class' occupations did pay more than working class ones. Now, someone with a traditionally working class job, such as a plumber or joiner, is likely to earn far more than a nurse or teacher, who would once have been considered lower middle class. The old classifications just don't apply today. Also, there are many people who work in offices (once a marker of the middle class) but have very little autonomy or job security, which used to signify working-class status. Similarly, salaried (ie monthly paid) roles are much more common than weekly paid ones, but don't confer 'staff' status in the way they once did.
All the same, 'the working class' or 'working people' usually means those who rely on working to get them through the month. If they didn't get paid (whether in wages or pension) they would struggle to afford the rent or mortgage for very long, and have little control over things like working hours, where they live and so on.