The working classes are those who are employed to create wealth for another member of society to benefit from.....
So anyone in employment is "working class"?
The problem is that the whole concept of "class" in Britain has been misunderstood for centuries, back to Magna Carta. It is not about income, and never has been. Rather it is more about the obligations and benefits one received. The "Upper Classes" owned the title to land, and could call upon their tenants to pay taxes and provide military service, but had the obligation to look after the interests of those tenants by maintaining the law and assisting them in times of difficulty. The "Middle Classes" - the yeomen - held property, smallholdings, and were obliged to pay the Lord for the use of the land, and provide military service. They employed workers, and were under the obligation to maintain their interests. The workers, a true "proletariat" who had no property other than their families, supplied labour and military manpower, in return for wages and protection. Movement between these strata was always possible in each direction, generally one way through education, te other through moral degradation. Generally this worked well until the industrial revolution and the urbanisation of the proletariat, when the ties with the land and the economic structure were severed. The working relationship was now based purely on payment with no reciprocal obligation (except when people tried to replicate the old system, such as in Saltaire).
This was totally different from the continental system, where the "nobles" were considered to own those beneath them in the pyramid. The various revolutions, and Marxism, all started from rejecting this premise. IMHO, this explains why a) there has never been such a workers revolution in this country, as the social structure was much more nuanced and b) why "class" is so misunderstood by those outside Britain looking in.
What we have lost since the early 1800s is much of the sense of obligations and duties, as we become more based on Money as a measure of worth in society. If "noblesse oblige" is brought up at all, it is there simply to be mocked; but it is the basis of much of our way of life, and could do with being brought back.