It's an old fashioned question because there's lots of social mobility now. Class is "class" as opposed to "socio-economic position" precisely because it denotes something you inherit. It refers to a certain culture that you are raised in, which itself used to be determined by job type.
I think that traditionally middle class have office jobs and earn a bit more. Because of this, they are usually people who went to university and go to shit like national trust - but it's not like those things make them middle class, it's just that they have the money and lifestyle for it. Working class have manual jobs and earn a bit less. Upper class have very good jobs or no job at all because they've inherited wealth or live from Investments.
In Austen's era, you'd have people with old money and gentry (upper class), self made money (merchant class) and manual labour (working class). It was hard to marry across the stratas, as marriages were orchestrated carefully, especially among the upper classes. University was for the wealthy. People inherited trades. So your job and related earnings was more than a job - it was an entire lifestyle, with associated rights, expectations, cultures, conduct codes.
Of course now you don't really get that anymore, because there's nothing stopping a kid whose parents work in a supermarket from going to university and becoming wealthy, or marrying into wealth. But you still have some slighter traces of the different "class cultures" in amongst the obvious lifestyle differences that come from office vs manual labourer jobs. So now you have the weird situation where people raised working class but in office jobs, or even people whose grandparents were working class, defining themselves as such. It's true if you hold fixed the cultures. It's not true if you're looking at it in terms of jobs and lifestyle. It's a matter of what you're using the terms to mean in the context you're interested in.
For what it's worth I think the real difference now in the UK, financially, socially and culturally, isn't between working class and middle class but between the "unemployed underclass" , the securely employed (working class + middle class), and the upper class (inherited wealth, trust fund and investment families).