Errr, isn't all of the West structured like that?
You're either the wealthy upper class who own the capital, land and means of production, or the middle class, responsible for keeping the upper class wealthy and in power(finance/law/consulting/politics) or the lower class, performing the basic services for the other two classes(building, cleaning, security, etc.)
AFAIK, that's how it works in most places on the planet including Europe and the US and it has been like that since a long time just that now the upper class has better PR.
And the opportunity to bridge through that income inequality (social mobility) is pretty low. France and a lot of Continental/EU Europe is far more equalitarian, better social system.
That's not the count of rough sleepers, though, that's more like 5000 to 8000.
(Also, IMO, what London has even more than income inequality is wealth inequality. House price appreciation has really added to it; it's not unusual to have little old ladies who are property millionaires, but their houses are decrepit piles of junk and they have no money to do them up. The housing stock is generally in dreadful shape, nowhere commensurate with the value of the land it's sitting on. Large sections of the capital are like this; decrepit, but very expensive.)
No, at least not all of it, not all of the time, and not as markedly, as you see in the UK.
The fact that you can not conceive this is possible, is telling in itself.
But I grew up and lived in several other Northern European countries where there is mostly just a huge middle class. Sure, some differences between upper-middle and lower-middle. But not a lot, and they can live side by side, go to the same school etc.
There are the odd billionaires, big estate heirs and royals i.e. classic upper-class but very few and they don't own everything. And they might also live near you, their kids might go to your normal public school etc. And then there are some unfortunate that could be classed as in a lower class but that is very few, and not everywhere, mostly just in the big cities. Mostly recent immigrants that do the jobs no-one else wants to do. They quickly get swallowed up by the middle class once settled.
Unless I was very sheltered that seems to be the case for most countries in Northern Europe apart from the UK?
Malnutrition! And Tower Hamlets is of course a 5 min walk to the very core of the City of London.
In the end, it’s a country that still has an official aristocracy. There is a reason for that.