Higher-middle and upper class more likely? Kids which need to earn their money usually go straight into apprenticeship or university and earn money promptly.
In the UK "upper class" is used almost exclusively for aristocrats. No matter how rich you are, unless there is a viable way for you to hold a title (e.g. Earl), you will not be considered upper class.
Middle class is basically anyone who does knowledge work and has aspirations of home ownership.
Your description of "Kids which need to earn their money usually go straight into apprenticeship or university and earn money promptly" would be very likely to be working class kids in the UK i.e. unlikely to be middle class.
Its a bit more complex in the UK ABc1 is middle but their are social distinctions dependant on job not income.
For example A Plumber Miner or train driver might make more than an engineer but would be working class.
Basically what sort of honour would you get for doing charity work is a good marker
Obviously it's easier with rich parents, but it doesn't really require as much cash as you're imagining. It's pretty common to work a little first then use all the cash to travel later for example, or to work while you travel, e.g. by teaching English (TEFL - https://www.tefl.org/blog/why-tefl-on-your-gap-year/).
The point is though - you don’t get anything at all until you actually attend classes. So taking a gap year means having to fund it yourself, or have generous parents but what this comments author describes is closer to ‘normal’ - a large number, not necessarily a majority, of 18year olds will plan out a gap year contingent on taking a part time job at some point and then using that to fund travel or something - before taking up a place on a course (and hence receiving the money)
If you have luck/motivation/connections/skillset - you might find a job related to your (future) degree too. I knew several people on my CS course who worked IT support at a local office for a few months whilst living with their parents - then set off on a backpacking trip somewhere exotic.
Everybody can have a loan for the full cost if they want one, people from poorer families get outright grants instead.
Certainly not perfect, but my impression is it hasn't significantly hindered uptake from lower income students and its not a major financial burden in practice.
Basically the GP is using the former definition and the person you're replying to is using the latter definition.
Crap on the Marxists all you want but they do at least have a fairly unambiguous taxonomy for these distinctions.
This is why any of these definitions get really murky, fast.
I think it is deeper than that, the country just has a confused relationship with the entire concept of class by both rejecting and embracing it.
On the other hand, someone who is worth, say, $10M or $20M is obviously still quite wealthy. But not necessarily in the doesn't need to think twice about hopping on a private plane or owning a private island category.
I actually oriented myself more on the numbers for Germany. Which means middle class is a single household with about 2000€ net income per month. That includes a lot of trade workers. It is perfectly possible to finance a gap year without or just minor parental support.
It used to be that it was more a thing for women, but that probably changed since draft was abandoned (before that the gap year for men would usually have been military service or alternative civilian service)