Does it really apply to UK students, though That's amazing if it does, but I'd imagine that it would depend on the university as well.
Just to clear up the who private vs. state, in the US, states are obliged to provide higher education for their young adults, which is why they set up 'state universities.' In effect, the state partly subsides the cost of tuition for 'in-state residents.' As a general rule, the 'state universities' cost less than the private universities -- even for out of state tuition. Of course, since private universities are no bound by this, they charge one rate.
I'm not too sure what sort of financial aid applies for a four-year course. Even if you apply to a UK university, especially if you are doing liberal arts, even participating in a UK-US exchange would benefit you enormously. The opportunity to study in the US, is such that...if you get the chance...do act upon it.
I am a history student, at the University of Plymouth and I took an exchange year to Idaho State University last year. I absolutely loved it, and often wish I can go back. There is much, much, much more Student finance help for you if you go down this route. Not to influence your university choice too much, but Plymouth University, offers direct exchanges with Plymouth State University (in New Hampshire), Mississippi (Ole Miss), Longwood (Virginia), Nebraska Wesleyan (a liberal arts college in Lincoln -- where the University of Nebraska is), Idaho State University and Montana State University. (Idaho State and Montana State are 'relatively close' being three-and-a-half hours away. Of course, if you still wanted to go to other universities, you can apply through ISEP which is essentially a UCAS to apply to American institutions on exchange. Of course, once you are at university, your exchange coordinator can help you out more. Most universities in the UK will offer exchange programs.
If you are interested, do have a look at Idaho State's program. You may or may not like it, but knowledge is power.
http://www.isu.edu/future/ ; there's a link at the bottom of the page which says 'request information.' I would recommend doing this a lot for a whole lot of institutions if you can.
I can only speak for their History and Political Science departments, but they have great teaching, and take their research very seriously. It's a Carnegie institution as well. If you still want to do Liberal Arts, I would also recommend Montana State as well. I've heard good things. I met a friend who applied directly to ISU for Economics, after he didn't get into Oxford. He did research on it, and found ISU's economics program above the likes of Exeter -- which is no mean feat.
Obviously, the more research you do, the easier it will be. Engage in the culture as much as you can, and also investigate other areas, such as the town and location. ISU is just over an hour from Salt Lake City. Also consider the climate and maybe start thinking of things you'll need. For a four year course at ISU For a four year course at
in the cheapest housing and with the cheapest meal plan, your looking at a ball park figure of $25,000 per semester -- or just a smidge over £16,000 per semester.
https://bigfuture.collegeboard.org/college-university-search/idaho-state-universityIf you go for four years, there's a whole bunch of stuff that you'd need to go through. The US VIsa that you'd need is a F-1 visa, which is more difficult to get. You'd need SAT scores and I think there's a few more that you'd have to take too. You may find that you'd need to get a job -- and there's a whole bunch of restrictions for 'aliens.'
Good luck though, and I wish you the best in your exams. Don't be disheartened too much by your GCSEs, but do try to improve them. Scholarship offers -- especially for international students -- are insanely competitive, so you need to stand out from the crowd.