In the UK education system, general education is considered completed by the age of 16, when students take their GCSEs (General Certificates of Secondary Education). That's supposedly the equivalent of a US high school diploma. After that, university-bound students or ones who want better qualifications take three or four (occasionally five) more subjects, which they study in-depth for either one year to earn an AS-level, or two years to earn an A-level. American AP exams are considered roughly equivalent to A-levels. When UK students go to university, they apply not just to the university but also to the programme they want, and their A-levels determine what programme they are eligible for. So if someone does A-levels in English, French, and Spanish, they could do a degree in any of those languages, or in Modern Languages or perhaps linguistics, but they couldn't do one in, say, biology. University courses last three years and are focused only on the degree subject. No general education requirements exist.
Basically, an American degree has more breadth, and a British one has more depth. According to some UK equivalencies, a US masters can be considered equivalent to a UK bachelors. For that reason also, things like law (and I think also medicine, but I'm not sure) require postgrad degrees in the US but are bachelors degrees in the UK. Then there's the whole "honours degree" thing, which frankly I think is a load of old tosh. My husband has a 2:2 "honours" degree, which I refuse to believe is any better than my cum laude, especially since he can't explain what makes an honours degree different from a standard one. NARIC would probably disagree with me, which is why I have never had them do an equivalency for my degree.
Frankly, the lack of respect the UK has for American degrees is one of my pet peeves, but unfortunately I don't think there's anything to be done about it. Is there any way you could do any kind of supplementary course or extra training to satisfy the requirement?