This is exactly right - it is done to reduce the building cost.
Of course having a ceiling this low is terrible for natural cooling so you then have to run air conditioning all the time costing far more in the long run. I live in a 1920s building with 11’ ceilings and I don’t have or need air conditioning because the place stays cool enough even through the height of summer.
The regulation is about energy efficiency of new-build construction, not how much you have your heating on. Partly it's a green thing, partly it's pragmatic, in that the UK has failed to invest in serious power generation for decades and faces the real possibility of brownouts in the not too distant future.
Plants are approaching EOL and they haven't been building new capacity to replace them. They've thrown a bunch of money at wind, but I think that's been more of a handout to (traditionally Conservative-voting) landowners than a viable strategy.
UK since middle ages was already infamous for having cities (specially london, but not just london) that have energetic problems and rely a lot on coal (and now other fossil fuels), leading to the infamous killer fogs, and to the victorian fashion (in victorian era, people tried to use stuff that would not have issues in a highly polluted air, for example extremely thick and dark curtains, so that people don't notice you aren't washing them a lot...)
Across Europe there are strict standards for building efficiency. This is not just about insufficient infrastructure, it's to keep energy waste in check. People want as cheap a house as possible (which I understand, it's hugely expensive and most people have to make serious sacrifices) and when having to choose between not terribly energy-inefficient and full-height bedrooms, they'll often choose the latter. Which is unsustainable in the aggregate. Hence, tight regulations on energy efficiency.
It's a the result of new of building code, which has minimum energy efficiency requirements. Residential energy efficiency is projected via heat loss calculations among other things.
Well, "should" or "shouldn't" can get too complex to analyze.
There's no god given set of rights -- what we get to do is what the era/society/legal system we live in allows us.
And what's moral/good to do even outside or against what's allowed, is a matter of philosophy.
People expected to be able to smoke even on an airplane in the 70s. Nowadays not so much. Asking someone not to smoke "within 30 ft of this building's entrance" (a common sign), would seem as ridiculous to them as the regulation of heating to you.
Huh, I grew up in a house with ceilings no higher than maybe 7'2" (though that was not usual for buildings) and am 5'11" and wouldn't dream of calling it "claustrophobic". My father is even a couple inches taller. I guess it depends a lot on what you're used to.
Meanwhile my current residence has ceilings so high that I haven't bothered to install some LED bulbs that I have lying around since I don't have an easy safe way to reach the light fixtures.
I am sure different people feel differently, but for me low ceilings are a non-option. In a climate like mine high ceilings avoid the need for air conditioning.
You can get special poles for changing high bulbs. I have seen them before, but I can't remember what they are called.
My house is 1860s with a 12' ceiling. Those other places feel like claustrophobic rabbit holes in comparison.
Low ceilings minimize material costs and maximize profits.