Earlier quoted context omitted.
> I've met several people in the UK who weren't able to study what they want because they had the wrong A-levels. // Presumably you mean weren't able to access the particular course+institution they wanted. Could you give some more details? It's a balance I suppose, either allow for early specialisation and get a head start or retain a broad spread and retain greater choice. That said I was able to do some Art Histor…
I admit I don't really know how the system works. My impression was that people can only study subjects they also had for A-Levels (or maybe related subjects, as defined by a university)? The people I met were all from UCL, so perhaps it was just that they wanted to get into specific universities and that made them compromise? Are the A-Levels really giving much of a head start? When I studied maths, it was really mu…
You're a bit limited with A levels, 'normal' load is 3, most undergrads in top institutions take 4 or even 5. I took a standard physics/engineer's load: double maths, physics and chemistry. I also took AS computing, but it bored the pants off me quite frankly. An ideal loadout for A level would be maths plus any two other subjects. I would be willing to be that most courses may overlook anything else, but maths is usually the bare requirement.
For science courses, you almost certainly have to have taken the pre-requisite A level. For non-science subjects, you don't need any particular qualifications besides a set of A levels at defined grade points. Some exceptions are for music, languages and arts where you'll probably have an entrance exam of some type. Oxbridge make applicants sit entrance papers for almost all subjects these days.
Point being - you only have to make compromises if the university you set your heart on forces it. Even Oxford and Cambridge generally don't specify subjects unless you're going for a science degree.
Maths/Further Maths was incredibly useful and coasted me through the first year of my degree. Most universities compensate for the fact that not all schools teach further maths (hence why first year physics is a cakewalk if you've done it). Standard maths is basic calculus, bit of series, that kind of thing. Further maths is much more advanced and introduces matrices, complex numbers, differential equations and higher levels of statistics and mechanics. Particularly for physics, knowing about matrices and complex numbers was a massive head start. At college you're still in rote-learning mode where someone shoves 100 equations in front of you and says "Solve". Most people don't have that kind of motivation at university, but it is incredibly effective at drilling in knowledge in something like maths.
The physics I learned at that time was fluff, chemistry and biology was memorisation. I can't speak for humanities, but languages seemed fairly rigorous and a big step up from secondary school.