I am going to try and take up a discriminatory case against my college and NHS for not providing me adequate study space.
As the saying goes, anyone can try to make a case of anything. It does help to be pragmatic, however, so one isn't spending their time (and those of other parties) on something that is not likely to be productive.
To start, you named NHS as one of the counter parties. Can you identify how NHS has an obligation to provide you with study space? If not, then perhaps they're not a relevant party.
Your other proposed counter party is your college. Do they have an obligation to provide a quiet study space?
This one is a bit more interesting.
Generally speaking, an educational institution's role is to provide education. As in instruction. In that sense, I don't see a direct connection.
That stated, most schools also offer resources, and that's where things get more interesting.
One such resource are libraries. Their main role is to provide access to books and other media. Again, there doesn't seem to be a clear connection.
With that stated, libraries can serve as a place to study, but what that means can vary.
It's not unusual for libraries to permit beverages in closed containers, for people to collaborate on projects, or even have food if discreet. Some libraries may have designated areas or rooms for this. Some libraries may desingate a quiet study room or area - if yours does not have one, perhaps you could make a proposal for and advicate for one.
One exception to the above is reference / archival libraries - where one accesses books that cannot be borrowed. In these libraries (which might form a floor or section of a larger general library), silence is the norm and sometimes even water bottles may not be permitted. They're not really intended to be general study spaces, but if you don't have one at home or elsewhere, perhaps that might work.
As Mary Terry suggested, some schools have faculty libraries and these often may be less used and quieter, and you may have access to them as a student even if not studying in a given faculty.